Journal of Geometry and Physics最新文献

{"title":"Outer billiards in the complex hyperbolic plane","authors":"Yamile Godoy,&nbsp;Marcos Salvai","doi":"10.1016/j.geomphys.2025.105544","DOIUrl":"10.1016/j.geomphys.2025.105544","url":null,"abstract":"<div><div>Given a quadratically convex compact connected oriented hypersurface <em>N</em> of the complex hyperbolic plane, we prove that the characteristic rays of the symplectic form restricted to <em>N</em> determine a double geodesic foliation of the exterior <em>U</em> of <em>N</em>. This induces an outer billiard map <em>B</em> on <em>U</em>. We prove that <em>B</em> is a diffeomorphism (notice that weaker notions of strict convexity may allow the billiard map to be well-defined and invertible, but not smooth) and moreover, a symplectomorphism. These results generalize known geometric properties of the outer billiard maps in the hyperbolic plane and complex Euclidean space.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105544"},"PeriodicalIF":1.6,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prequantization of differential characters of Lie groupoids","authors":"Cheng-Yong Du","doi":"10.1016/j.geomphys.2025.105547","DOIUrl":"10.1016/j.geomphys.2025.105547","url":null,"abstract":"<div><div>In this paper, we describe a category <span><math><msubsup><mrow><mi>DC</mi></mrow><mrow><mrow><mi>ex</mi></mrow><mo>,</mo><mn>3</mn><mo>−</mo><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of degree-3 differential characters of a Lie groupoid <span><math><mi>G</mi></math></span> together with a prequantization functor Preq from it to the category <span><math><mi>G</mi><mi>e</mi><mi>r</mi><msub><mrow><mi>b</mi></mrow><mrow><mi>∇</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-central extensions with pseudo-connections over <span><math><mi>G</mi></math></span>, and show that Preq is an equivalence of categories and the isomorphism classes of <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-central extensions with pseudo-connections over <span><math><mi>G</mi></math></span> are classified by the cohomology group <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>(</mo><mi>D</mi><msubsup><mrow><mi>C</mi></mrow><mrow><mrow><mi>ex</mi></mrow><mo>,</mo><mn>3</mn><mo>−</mo><mn>1</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span> of degree-3 differential characters. As an application, we characterize closed integral 3-forms with prequantization <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-central extensions and pseudo-connections for all Lie groupoids. This generalizes Behrend–Xu's prequantization result of degree 3-context for Lie groupoids satisfying <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mo>•</mo></mrow></msub><mo>)</mo><mo>,</mo><mo>∂</mo><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. Moreover we identify the group of flat <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-central extensions over a Lie groupoid <span><math><mi>G</mi></math></span> with the cohomology group <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>ex</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>,</mo><mi>R</mi><mo>/</mo><mi>Z</mi><mo>)</mo><mo>)</mo></math></span> of a modification of the complex of singular cochains with coefficient in <span><math><mi>R</mi><mo>/</mo><mi>Z</mi></math></span>. We also extend these results to differentiable stacks.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105547"},"PeriodicalIF":1.6,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representations and cohomology of Rota-Baxter Lie conformal algebras","authors":"Jun Zhao ,&nbsp;Bing Sun ,&nbsp;Liangyun Chen","doi":"10.1016/j.geomphys.2025.105542","DOIUrl":"10.1016/j.geomphys.2025.105542","url":null,"abstract":"<div><div>In this paper, we study representations and cohomology of a weighted Rota-Baxter Lie conformal algebra. Given a weighted Rota-Baxter Lie conformal algebra <span><math><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></span> and its representation <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span>, we define its cohomology and discuss the relation with the cohomology of weighted Rota-Baxter associative conformal algebra. As applications of the cohomology theory, we study abelian extensions, formal deformations of a weighted Rota-Baxter Lie conformal algebra.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105542"},"PeriodicalIF":1.6,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrability structures of the (2 + 1)-dimensional Euler equation","authors":"I.S. Krasil′shchik,&nbsp;O.I. Morozov","doi":"10.1016/j.geomphys.2025.105543","DOIUrl":"10.1016/j.geomphys.2025.105543","url":null,"abstract":"<div><div>We construct a local variational Poisson structure (a Hamiltonian operator) for the <span><math><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional Euler equation in vorticity form. The inverse defines a nonlocal symplectic structure for the equation. We describe the action of this operator on the infinitesimal contact symmetries in terms of differential coverings over the Euler equation. Furthermore, we construct a nonlocal recursion operator for cosymmetries. Finally, we generalize the local variational Poisson structure for the Euler equation in vorticity form on a two-dimensional Riemannian manifold.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105543"},"PeriodicalIF":1.6,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algebro-geometric initial value problems for integrable nonlinear lattices: Tetragonal curves and Riemann theta function solutions","authors":"Xianguo Geng,&nbsp;Minxin Jia,&nbsp;Ruomeng Li","doi":"10.1016/j.geomphys.2025.105541","DOIUrl":"10.1016/j.geomphys.2025.105541","url":null,"abstract":"<div><div>In this paper, we establish the theory of tetragonal curves and address a series of fundamental problems within this framework, including the construction of a basis for holomorphic Abelian differentials, Abelian differentials of the second and third kinds, Baker-Akhiezer functions, and meromorphic functions. Building on these results, we apply the theory of tetragonal curves to investigate algebro-geometric initial value problems for integrable nonlinear lattice systems. As an illustrative example, we employ the discrete zero-curvature equation and the discrete Lenard equation to derive a hierarchy of coupled Bogoyavlensky lattice equations associated with a discrete <span><math><mn>4</mn><mo>×</mo><mn>4</mn></math></span> matrix spectral problem. By analyzing the characteristic polynomial of the Lax matrix for this hierarchy, we introduce a tetragonal curve and its associated Riemann theta function, exploring the algebro-geometric properties of Baker-Akhiezer functions and a class of meromorphic functions. Using the Abel map and Abelian differentials, we precisely straighten out various flows. Finally, we obtain Riemann theta function solutions for the algebro-geometric initial value problems of the entire coupled Bogoyavlensky lattice hierarchy.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105541"},"PeriodicalIF":1.6,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus three","authors":"Shigeki Matsutani","doi":"10.1016/j.geomphys.2025.105540","DOIUrl":"10.1016/j.geomphys.2025.105540","url":null,"abstract":"<div><div>The real and imaginary parts of the focusing modified Korteweg-de Vries (MKdV) equation defined over the complex field <span><math><mi>C</mi></math></span> give rise to the focusing gauged MKdV (FGMKdV) equations. As a generalization of Euler's elastica whose curvature obeys the focusing static MKdV (FSMKdV) equation, we study real plane curves whose curvature obeys the FGMKdV equation since the FSMKdV equation is a special case of the FGMKdV equation. In this paper, we focus on the hyperelliptic curves of genus three. By tuning some moduli parameters and initial conditions, we show closed real plane curves associated with the FGMKdV equation beyond Euler's figure-eight of elastica.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105540"},"PeriodicalIF":1.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mirror partner for a Klein quartic polynomial","authors":"Alexey Basalaev","doi":"10.1016/j.geomphys.2025.105538","DOIUrl":"10.1016/j.geomphys.2025.105538","url":null,"abstract":"<div><div>The results of A. Chiodo, Y. Ruan and M. Krawitz associate the mirror partner Calabi–Yau variety <em>X</em> to a Landau–Ginzburg orbifold <span><math><mo>(</mo><mi>f</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> if <em>f</em> is an invertible polynomial satisfying Calabi–Yau condition and the group <em>G</em> is a diagonal symmetry group of <em>f</em>. In this paper we investigate the Landau–Ginzburg orbifolds with a Klein quartic polynomial <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <em>G</em> being all possible subgroups of <span><math><mrow><mi>GL</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>, preserving the polynomial <em>f</em> and also the pairing in its Jacobian algebra. In particular, <em>G</em> is not necessarily abelian or diagonal. The zero–set of polynomial <em>f</em>, called Klein quartic, is a genus 3 smooth compact Riemann surface. We show that its mirror Landau–Ginzburg orbifold is <span><math><mo>(</mo><mi>f</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> with <em>G</em> being a <span><math><mi>Z</mi><mo>/</mo><mn>2</mn><mi>Z</mi></math></span>–extension of a Klein four–group.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105538"},"PeriodicalIF":1.6,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrable geometric evolution equations through a deformed Heisenberg spin equation","authors":"Dae Won Yoon ,&nbsp;Zühal Küçükarslan Yüzbaşı","doi":"10.1016/j.geomphys.2025.105534","DOIUrl":"10.1016/j.geomphys.2025.105534","url":null,"abstract":"<div><div>Using the geometrical equivalence methods, we showed a deformed Heisenberg spin chain equation is geometrically equivalent to a generalized nonlinear Schrödinger equation. After that, we demonstrate in Euclidean 3-space that assigning spin vectors to the tangent, normal, and binormal vectors of the three distinct moving space curves, respectively, results in the creation of three distinct surfaces. Then we find the Gauss and the mean curvatures of these surfaces, respectively.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105534"},"PeriodicalIF":1.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moduli spaces of weighted pointed stable curves and toric topology of Grassmann manifolds","authors":"Victor M. Buchstaber ,&nbsp;Svjetlana Terzić","doi":"10.1016/j.geomphys.2025.105533","DOIUrl":"10.1016/j.geomphys.2025.105533","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we establish fundamental relations between the famous problem of compactifications of the moduli space &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of ordered &lt;em&gt;n&lt;/em&gt; distinct points on &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and toric topology of the complex Grassmann manifolds &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The best known is the Deligne-Mumford compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The Losev-Manin compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is also closely related to important questions in mathematical physics and toric geometry. These compactifications belong to the family of Hassett compactifications &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of moduli spaces of weighted pointed stable curves. In this paper we show that the orbit space &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; of complex Grassmann manifolds &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; by the canonical action of the compact torus &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; of the complexity &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; serves as a universal space in a sense that for any Hassett compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; there exists a subspace &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and birational morphism &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. We describe large class of the set of weights &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for which this birational morphism gives rise to an isomorphism. This provides topological model for the Hassett category in which Deligne-Mumford compactification &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"215 ","pages":"Article 105533"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral forms and de-Rham Hodge operator","authors":"Jian Wang ,&nbsp;Yong Wang ,&nbsp;Mingyu Liu","doi":"10.1016/j.geomphys.2025.105535","DOIUrl":"10.1016/j.geomphys.2025.105535","url":null,"abstract":"<div><div>Motivated by the trilinear functional of differential one-forms, spectral triple and spectral torsion for the Hodge-Dirac operator, we introduce a multilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue, which generalize the spectral torsion defined by Dabrowski-Sitarz-Zalecki. The main results of this paper recover two forms, torsion of the linear connection and four forms by the noncommutative residue and perturbed de-Rham Hodge operators, and provide an explicit computation of generalized spectral forms associated with the perturbed de-Rham Hodge Dirac triple.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"214 ","pages":"Article 105535"},"PeriodicalIF":1.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}