Advances in Mathematics最新文献

{"title":"A short proof of a conjecture of Matsushita","authors":"Benjamin Bakker","doi":"10.1016/j.aim.2025.110554","DOIUrl":"10.1016/j.aim.2025.110554","url":null,"abstract":"<div><div>We build on the arguments of van Geemen and Voisin <span><span>[24]</span></span> to prove a conjecture of Matsushita that a Lagrangian fibration of an irreducible hyperkähler manifold is either isotrivial or of maximal variation. We also complete a partial result of Voisin <span><span>[26]</span></span> regarding the density of torsion points of sections of Lagrangian fibrations.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"482 ","pages":"Article 110554"},"PeriodicalIF":1.5,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth representations of affine Kac-Moody algebras","authors":"V. Futorny ,&nbsp;X. Guo ,&nbsp;Y. Xue ,&nbsp;K. Zhao","doi":"10.1016/j.aim.2025.110559","DOIUrl":"10.1016/j.aim.2025.110559","url":null,"abstract":"<div><div>Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras. But, very little is known about such modules beyond the category of positive energy representations. We construct a new class of smooth modules over affine Kac-Moody algebras. In a particular case, these modules are isomorphic to those induced from generalized Whittaker modules for Takiff Lie algebras. We establish the irreducibility criterion for constructed modules in the case of the Lie algebra <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110559"},"PeriodicalIF":1.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Hitchin fibration for symmetric pairs","authors":"Thomas Hameister,&nbsp;Benedict Morrissey","doi":"10.1016/j.aim.2025.110560","DOIUrl":"10.1016/j.aim.2025.110560","url":null,"abstract":"<div><div>We introduce and describe the “regular quotient” for the Hitchin fibration for symmetric spaces and explain some basic consequences for Higgs bundles. We include an invariant theoretic approach to spectral covers in this setting for the particular space <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>/</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We also include a study of the regular centralizer group scheme for quasisplit pairs, including a Galois description of a closely related group scheme. We collect some basic consequences for Hitchin systems associated to such pairs.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"482 ","pages":"Article 110560"},"PeriodicalIF":1.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence and collapsing of CAT(0)-lattices","authors":"Nicola Cavallucci ,&nbsp;Andrea Sambusetti","doi":"10.1016/j.aim.2025.110555","DOIUrl":"10.1016/j.aim.2025.110555","url":null,"abstract":"<div><div>We study the theory of convergence for CAT(0)-lattices (that is groups Γ acting geometrically on proper, geodesically complete CAT(0)-spaces) and their quotients (CAT(0)-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how the actions can degenerate to a possibly non-discrete limit action, and prove a compactness theorem for the class of compact CAT(0)-homology orbifolds. Finally, as an application of this theory, we prove an isolation result for flat orbispaces and an entropy-pinching theorem.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"482 ","pages":"Article 110555"},"PeriodicalIF":1.5,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145189999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Instantaneous continuous loss of regularity for the SQG equation","authors":"Diego Córdoba ,&nbsp;Luis Martínez-Zoroa ,&nbsp;Wojciech S. Ożański","doi":"10.1016/j.aim.2025.110553","DOIUrl":"10.1016/j.aim.2025.110553","url":null,"abstract":"<div><div>Given <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>, we construct a compactly supported initial data <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> such that <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></mrow></msub><mo>≤</mo><mi>ε</mi></math></span> and there exist <span><math><mi>T</mi><mo>&gt;</mo><mn>0</mn></math></span>, <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span> and a local-in-time solution <em>θ</em> of the SQG equation that is compactly supported in space, continuous and differentiable in <em>t</em> and in <em>x</em> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></math></span>, and, for each <span><math><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></math></span>, <span><math><mi>θ</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi><mo>/</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>c</mi><mi>t</mi><mo>)</mo></mrow></msup></math></span> and <span><math><mi>θ</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>t</mi><mo>)</mo><mo>∉</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span> for any <span><math><mi>β</mi><mo>&gt;</mo><mi>s</mi><mo>/</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>c</mi><mi>t</mi><mo>)</mo></math></span>. Moreover, <em>θ</em> is unique among all solutions with initial condition <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> which belong to <span><math><mi>C</mi><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>;</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>δ</mi></mrow></msup><mo>)</mo></math></span> for any <span><math><mi>δ</mi><mo>&gt;</mo><mn>0</mn></math></span> and is continuous and differentiable in <em>t</em> and in <em>x</em> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110553"},"PeriodicalIF":1.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extendability of foliations","authors":"Pablo Perrella ,&nbsp;Sebastián Velazquez","doi":"10.1016/j.aim.2025.110538","DOIUrl":"10.1016/j.aim.2025.110538","url":null,"abstract":"<div><div>Given a foliation F on X and an embedding <span><math><mi>X</mi><mo>⊆</mo><mi>Y</mi></math></span>, is there a foliation on Y extending F? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently positive with respect to <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> and the singularities of F belong to a certain class. These tools also apply in the case where Y is the total space of a deformation of X. Regarding the uniqueness of the extension, we prove a foliated version of a statement by Fujita and Grauert ensuring the existence of tubular neighborhoods. We also give sufficient conditions for a foliation to have only trivial unfoldings, generalizing a result due to Gómez-Mont.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110538"},"PeriodicalIF":1.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational principles for Hausdorff and packing dimensions of fractal percolation on self-affine sponges","authors":"Julien Barral,&nbsp;Guilhem Brunet","doi":"10.1016/j.aim.2025.110549","DOIUrl":"10.1016/j.aim.2025.110549","url":null,"abstract":"<div><div>We establish variational principles for the Hausdorff and packing dimensions of a class of statistically self-affine sponges, including in particular fractal percolation sets obtained from Barański and Gatzouras-Lalley carpets and sponges. Our first step is to compute the Hausdorff and packing dimensions of non-degenerate inhomogeneous Mandelbrot measures supported on the associated random limit sets. This is not a straightforward combination of the existing approaches for the deterministic inhomogeneous Bernoulli measures and the Mandelbrot measures on random Sierpiński sponges; it reveals new structural features. The variational principles rely on a specific subclass of inhomogeneous Mandelbrot measures, which are connected to localized digit frequencies in the underlying coding space. This connection makes it possible to construct effective coverings of the random limit set, leading to sharp upper bounds for its Hausdorff and packing dimensions.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110549"},"PeriodicalIF":1.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The consistency strength of determinacy when all sets are universally Baire","authors":"Sandra Müller","doi":"10.1016/j.aim.2025.110548","DOIUrl":"10.1016/j.aim.2025.110548","url":null,"abstract":"<div><div>It is known that the large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is much stronger than the Axiom of Determinacy itself. Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson used a generalization of Woodin's derived model construction to show that this conjectured result would be optimal. In this paper we introduce a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and apply it to prove Sargsyan's conjecture.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110548"},"PeriodicalIF":1.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solution of all quartic matrix models","authors":"Harald Grosse ,&nbsp;Alexander Hock ,&nbsp;Raimar Wulkenhaar","doi":"10.1016/j.aim.2025.110551","DOIUrl":"10.1016/j.aim.2025.110551","url":null,"abstract":"<div><div>We consider the quartic analogue of the Kontsevich model, which is defined by a measure <span><math><mi>exp</mi><mo>⁡</mo><mo>(</mo><mo>−</mo><mi>N</mi><mspace></mspace><mrow><mi>Tr</mi></mrow><mo>(</mo><mi>E</mi><msup><mrow><mi>Φ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>(</mo><mi>λ</mi><mo>/</mo><mn>4</mn><mo>)</mo><msup><mrow><mi>Φ</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo><mo>)</mo><mi>d</mi><mi>Φ</mi></math></span> on Hermitian <span><math><mi>N</mi><mo>×</mo><mi>N</mi></math></span>-matrices, where <em>E</em> is any positive matrix and <em>λ</em> a scalar. It was previously established that the large-<em>N</em> limit of the second moment (the planar two-point function) satisfies a non-linear integral equation. By employing tools from complex analysis, in particular the Lagrange-Bürmann inversion formula, we identify the exact solution of this non-linear problem, both for finite <em>N</em> and for a large-<em>N</em> limit to unbounded operators <em>E</em> of spectral dimension ≤4. For finite <em>N</em>, the two-point function is a rational function evaluated at the preimages of another rational function <em>R</em> constructed from the spectrum of <em>E</em>. Subsequent work has constructed from this formula a family <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span> of meromorphic differentials which obey blobbed topological recursion. For unbounded operators <em>E</em>, the renormalised two-point function is given by an integral formula involving a regularisation of <em>R</em>. This allowed a proof, in subsequent work, that the <span><math><mi>λ</mi><msubsup><mrow><mi>Φ</mi></mrow><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></msubsup></math></span>-model on noncommutative Moyal space does not have a triviality problem.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110551"},"PeriodicalIF":1.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear Reedy categories, quasi-hereditary algebras and model structures","authors":"Georgios Dalezios ,&nbsp;Jan Šťovíček","doi":"10.1016/j.aim.2025.110550","DOIUrl":"10.1016/j.aim.2025.110550","url":null,"abstract":"<div><div>We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category <span><math><mi>C</mi></math></span> over a field, the category of left <span><math><mi>C</mi></math></span>–modules admits a highest weight structure, which in case <span><math><mi>C</mi></math></span> is finite corresponds to a quasi-hereditary algebra with an exact Borel subalgebra. We also lift complete cotorsion pairs and abelian model structures to certain categories of additive functors indexed by linear Reedy categories, generalizing analogous results from the hereditary case.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"481 ","pages":"Article 110550"},"PeriodicalIF":1.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}