Journal of Geometry and Physics最新文献_第4页

Additional symmetries for the N=2 supersymmetric Two-Boson hierarchy and the multi-component generalization

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-18 DOI: 10.1016/j.geomphys.2025.105455

Jian Li , Chuanzhong Li

引用次数: 0

Separation of variables for the Clebsch model: so(4) spectral/separation curves

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-18 DOI: 10.1016/j.geomphys.2025.105453

T. Skrypnyk

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Local systems of Castelnuovo-type and factorization of semistable families

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-18 DOI: 10.1016/j.geomphys.2025.105452

Luca Rizzi , Francesco Zucconi

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Constantly curved holomorphic two-spheres in the complex Grassmannian G(2,6) with constant square norm of the second fundamental form

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-17 DOI: 10.1016/j.geomphys.2025.105451

Jie Fei , Ling He , Jun Wang

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A purely analytic derivation of Bonnet surfaces

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-17 DOI: 10.1016/j.geomphys.2025.105454

Robert Conte , Alfred Michel Grundland

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Virtual classes of character stacks

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-14 DOI: 10.1016/j.geomphys.2025.105450

Ángel González-Prieto , Márton Hablicsek , Jesse Vogel

{"title":"Virtual classes of character stacks","authors":"Ángel González-Prieto , Márton Hablicsek , Jesse Vogel","doi":"10.1016/j.geomphys.2025.105450","DOIUrl":"10.1016/j.geomphys.2025.105450","url":null,"abstract":"<div><div>In this paper, we extend the Topological Quantum Field Theory developed by González-Prieto, Logares, and Muñoz for computing virtual classes of <em>G</em>-representation varieties of closed orientable surfaces in the Grothendieck ring of varieties to the setting of the character stacks. To this aim, we define a suitable Grothendieck ring of representable stacks, over which this Topological Quantum Field Theory is defined. In this way, we compute the virtual class of the character stack over B<em>G</em>, that is, a motivic decomposition of the representation variety with respect to the natural adjoint action.</div><div>We apply this framework in two cases providing explicit expressions for the virtual classes of the character stacks of closed orientable surfaces of arbitrary genus. First, in the case of the affine linear group of rank 1, the virtual class of the character stack fully remembers the natural adjoint action, in particular, the virtual class of the character variety can be straightforwardly derived. Second, we consider the non-connected group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>⋊</mo><mi>Z</mi><mo>/</mo><mn>2</mn><mi>Z</mi></math></span>, and we show how our theory allows us to compute motivic information of the character stacks where the classical naïve point-counting method fails.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"211 ","pages":"Article 105450"},"PeriodicalIF":1.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The generic étaleness of the moduli space of dormant so2ℓ-opers

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-05 DOI: 10.1016/j.geomphys.2025.105439

Yasuhiro Wakabayashi

{"title":"The generic étaleness of the moduli space of dormant so2ℓ-opers","authors":"Yasuhiro Wakabayashi","doi":"10.1016/j.geomphys.2025.105439","DOIUrl":"10.1016/j.geomphys.2025.105439","url":null,"abstract":"<div><div>The generic étaleness is an important property on the moduli space of dormant <span><math><mi>g</mi></math></span>-opers (for a simple Lie algebra <span><math><mi>g</mi></math></span>) in the context of enumerative geometry. In the previous study, this property has been verified under the assumption that <span><math><mi>g</mi></math></span> is either <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>so</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>, or <span><math><msub><mrow><mi>sp</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub></math></span> for any sufficiently small positive integer <em>ℓ</em>. The purpose of the present paper is to prove the generic étaleness for one of the remaining cases, i.e., <span><math><mi>g</mi><mo>=</mo><msub><mrow><mi>so</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub></math></span>. As an application of this result, we obtain a factorization formula for computing the generic degree induced from pull-back along various clutching morphisms between moduli spaces of pointed stable curves.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"211 ","pages":"Article 105439"},"PeriodicalIF":1.6,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396035","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}

引用次数: 0

Local realizations of vertex algebras

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-02-05 DOI: 10.1016/j.geomphys.2025.105440

Peng Wang, Liangyun Chen

引用次数: 0

Relating Hamiltonian systems with multiple invariants to generalized Hamiltonian mechanics via multisymplectic geometry

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-01-30 DOI: 10.1016/j.geomphys.2025.105438

Nathan Duignan , Naoki Sato

{"title":"Relating Hamiltonian systems with multiple invariants to generalized Hamiltonian mechanics via multisymplectic geometry","authors":"Nathan Duignan , Naoki Sato","doi":"10.1016/j.geomphys.2025.105438","DOIUrl":"10.1016/j.geomphys.2025.105438","url":null,"abstract":"<div><div>Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, ‘hides’ other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to generalize classical Hamiltonian mechanics to ideal dynamical systems bearing two Hamiltonians, but its connection to a suitable geometric framework has remained elusive. This work establishes a novel correspondence between generalized Hamiltonian mechanics, defined for systems with a phase space conservation law (invariance of a closed form) and a matter conservation law (invariance of multiple Hamiltonians), and classical Hamiltonian mechanics via multisymplectic geometry. The key lies in the invertibility of differential forms of degree higher than 2. We demonstrate that the cornerstone theorems of classical Hamiltonian mechanics (Lie-Darboux and Liouville) require reinterpretation within this new framework, reflecting the unique properties of invertibility in multisymplectic geometry. Furthermore, we present two key theorems that solidify the connection: i) any classical Hamiltonian system with two or more invariants is also a generalized Hamiltonian system and ii) given a generalized Hamiltonian system with two or more invariants, there exists a corresponding classical Hamiltonian system on the level set of all but one invariant, with the remaining invariant playing the role of the Hamiltonian function.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"211 ","pages":"Article 105438"},"PeriodicalIF":1.6,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The three-point Gaudin model and branched coverings of the Riemann sphere

IF 1.6 3区数学

Journal of Geometry and Physics Pub Date : 2025-01-27 DOI: 10.1016/j.geomphys.2025.105436

Natalia Amburg , Ilya Tolstukhin

引用次数: 0