Forum of Mathematics Sigma最新文献

{"title":"O’Grady tenfolds as moduli spaces of sheaves","authors":"Camilla Felisetti, Franco Giovenzana, Annalisa Grossi","doi":"10.1017/fms.2024.46","DOIUrl":"https://doi.org/10.1017/fms.2024.46","url":null,"abstract":"We give a lattice-theoretic characterization for a manifold of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400046X_inline1.png\"/> <jats:tex-math> $operatorname {mathrm {OG10}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li–Pertusi–Zhao variety of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400046X_inline2.png\"/> <jats:tex-math> $operatorname {mathrm {OG10}}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deformations of Calabi–Yau varieties with k-liminal singularities","authors":"Robert Friedman, Radu Laza","doi":"10.1017/fms.2024.44","DOIUrl":"https://doi.org/10.1017/fms.2024.44","url":null,"abstract":"The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000446_inline1.png\"/> <jats:tex-math> $4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. For nodal Calabi–Yau threefolds, a necessary and sufficient linear topological condition for the existence of a first-order smoothing was first given in [Fri86]. Subsequently, Rollenske–Thomas [RT09] generalized this picture to nodal Calabi–Yau varieties of odd dimension by finding a necessary nonlinear topological condition for the existence of a first-order smoothing. In a complementary direction, in [FL22a], the linear necessary and sufficient conditions of [Fri86] were extended to Calabi–Yau varieties in every dimension with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000446_inline2.png\"/> <jats:tex-math> $1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-liminal singularities (which are exactly the ordinary double points in dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000446_inline3.png\"/> <jats:tex-math> $3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> but not in higher dimensions). In this paper, we give a common formulation of all of these previous results by establishing analogues of the nonlinear topological conditions of [RT09] for Calabi–Yau varieties with weighted homogeneous <jats:italic>k</jats:italic>-liminal hypersurface singularities, a broad class of singularities that includes ordinary double points in odd dimensions.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimal subdynamics and minimal flows without characteristic measures","authors":"Joshua Frisch, Brandon Seward, Andy Zucker","doi":"10.1017/fms.2024.41","DOIUrl":"https://doi.org/10.1017/fms.2024.41","url":null,"abstract":"Given a countable group <jats:italic>G</jats:italic> and a <jats:italic>G</jats:italic>-flow <jats:italic>X</jats:italic>, a probability measure <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000410_inline1.png\"/> <jats:tex-math> $mu $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> on <jats:italic>X</jats:italic> is called characteristic if it is <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000410_inline2.png\"/> <jats:tex-math> $mathrm {Aut}(X, G)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-invariant. Frisch and Tamuz asked about the existence of a minimal <jats:italic>G</jats:italic>-flow, for any group <jats:italic>G</jats:italic>, which does not admit a characteristic measure. We construct for every countable group <jats:italic>G</jats:italic> such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group <jats:italic>G</jats:italic> and a collection of infinite subgroups <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000410_inline3.png\"/> <jats:tex-math> ${Delta _i: iin I}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, when is there a faithful <jats:italic>G</jats:italic>-flow for which every <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000410_inline4.png\"/> <jats:tex-math> $Delta _i$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> acts minimally?","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration","authors":"Matteo Mucciconi, Makiko Sasada, Tomohiro Sasamoto, Hayate Suda","doi":"10.1017/fms.2024.39","DOIUrl":"https://doi.org/10.1017/fms.2024.39","url":null,"abstract":"The box-ball system (BBS), which was introduced by Takahashi and Satsuma in 1990, is a soliton cellular automaton. Its dynamics can be linearized by a few methods, among which the best known is the Kerov–Kirillov–Reschetikhin (KKR) bijection using rigged partitions. Recently, a new linearization method in terms of ‘slot configurations’ was introduced by Ferrari–Nguyen–Rolla–Wang, but its relations to existing ones have not been clarified. In this paper, we investigate this issue and clarify the relation between the two linearizations. For this, we introduce a novel way of describing the BBS dynamics using a carrier with seat numbers. We show that the seat number configuration also linearizes the BBS and reveals explicit relations between the KKR bijection and the slot configuration. In addition, by using these explicit relations, we also show that even in case of finite carrier capacity the BBS can be linearized via the slot configuration.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A short proof of the Hanlon-Hicks-Lazarev Theorem","authors":"Michael K. Brown, Daniel Erman","doi":"10.1017/fms.2024.40","DOIUrl":"https://doi.org/10.1017/fms.2024.40","url":null,"abstract":"We give a short new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virtual resolutions and to a resolution of the diagonal in the simplicial case.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Ceresa class and tropical curves of hyperelliptic type","authors":"Daniel Corey, Wanlin Li","doi":"10.1017/fms.2024.36","DOIUrl":"https://doi.org/10.1017/fms.2024.36","url":null,"abstract":"We define a new algebraic invariant of a graph <jats:italic>G</jats:italic> called the Ceresa–Zharkov class and show that it is trivial if and only if <jats:italic>G</jats:italic> is of hyperelliptic type, equivalently, <jats:italic>G</jats:italic> does not have as a minor the complete graph on four vertices or the loop of three loops. After choosing edge lengths, this class specializes to an algebraic invariant of a tropical curve with underlying graph <jats:italic>G</jats:italic> that is closely related to the Ceresa cycle for an algebraic curve defined over <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000367_inline1.png\"/> <jats:tex-math> $mathbb {C}(!(t)!)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Affine Bruhat order and Demazure products","authors":"Felix Schremmer","doi":"10.1017/fms.2024.33","DOIUrl":"https://doi.org/10.1017/fms.2024.33","url":null,"abstract":"We give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph. These results can be understood to describe certain closure relations concerning the Iwahori–Bruhat decomposition of an algebraic group. As an application towards affine Deligne–Lusztig varieties, we present a new formula for generic Newton points.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An extension of the stochastic sewing lemma and applications to fractional stochastic calculus","authors":"Toyomu Matsuda, Nicolas Perkowski","doi":"10.1017/fms.2024.32","DOIUrl":"https://doi.org/10.1017/fms.2024.32","url":null,"abstract":"We give an extension of Lê’s stochastic sewing lemma. The stochastic sewing lemma proves convergence in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline1.png\" /> <jats:tex-math> $L_m$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of Riemann type sums <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline2.png\" /> <jats:tex-math> $sum _{[s,t] in pi } A_{s,t}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for an adapted two-parameter stochastic process <jats:italic>A</jats:italic>, under certain conditions on the moments of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline3.png\" /> <jats:tex-math> $A_{s,t}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and of conditional expectations of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline4.png\" /> <jats:tex-math> $A_{s,t}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> given <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline5.png\" /> <jats:tex-math> $mathcal F_s$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Our extension replaces the conditional expectation given <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline6.png\" /> <jats:tex-math> $mathcal F_s$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> by that given <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline7.png\" /> <jats:tex-math> $mathcal F_v$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline8.png\" /> <jats:tex-math> $v&lt;s$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, and it allows to make use of asymptotic decorrelation properties between <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline9.png\" /> <jats:tex-math> $A_{s,t}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S205050942400032X_inline10.png\" /> <jats:tex-math> $mathcal F_v$ </jats:t","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generic Stability Independence and Treeless Theories","authors":"Itay Kaplan, Nicholas Ramsey, Pierre Simon","doi":"10.1017/fms.2024.35","DOIUrl":"https://doi.org/10.1017/fms.2024.35","url":null,"abstract":"We initiate a systematic study of <jats:italic>generic stability independence</jats:italic> and introduce the class of <jats:italic>treeless theories</jats:italic> in which this notion of independence is particularly well behaved. We show that the class of treeless theories contains both binary theories and stable theories and give several applications of the theory of independence for treeless theories. As a corollary, we show that every binary NSOP<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000355_inline1.png\" /> <jats:tex-math> $_{3}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> theory is simple.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generic Beauville’s Conjecture","authors":"Izzet Coskun, Eric Larson, Isabel Vogt","doi":"10.1017/fms.2024.21","DOIUrl":"https://doi.org/10.1017/fms.2024.21","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000215_inline1.png\" /> <jats:tex-math> $alpha colon X to Y$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000215_inline2.png\" /> <jats:tex-math> $alpha $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is semistable if the genus of <jats:italic>Y</jats:italic> is at least <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000215_inline3.png\" /> <jats:tex-math> $1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and stable if the genus of <jats:italic>Y</jats:italic> is at least <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000215_inline4.png\" /> <jats:tex-math> $2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We prove this conjecture if the map <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000215_inline5.png\" /> <jats:tex-math> $alpha $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is general in any component of the Hurwitz space of covers of an arbitrary smooth curve <jats:italic>Y</jats:italic>.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}