Splitting invariants are effective for distinguishing the embedded topology of plane curves. In this note, we introduce a generalization of splitting invariants, called the G-combinatorial type, for plane curves by using the modified plumbing graph defined by Hironaka [14]. We prove that the G-combinatorial type is invariant under certain homeomorphisms based on the arguments of Waldhausen [32, 33] and Neumann [22]. Furthermore, we distinguish the embedded topology of quasi-triangular curves by the G-combinatorial type, which are generalization of triangular curves studied in [4].
分裂不变式可以有效区分平面曲线的嵌入拓扑。在本注释中，我们使用 Hironaka [14] 定义的改进垂线图，为平面曲线引入了一种广义的分裂不变式，称为 G 组合类型。我们基于 Waldhausen [32, 33] 和 Neumann [22] 的论证，证明了 G 组合类型在某些同构下是不变的。此外，我们用 G 组合类型区分了准三角形曲线的嵌入拓扑，它们是 [4] 中研究的三角形曲线的一般化。
{"title":"A note on combinatorial type and splitting invariants of plane curves","authors":"Taketo Shirane","doi":"arxiv-2409.07915","DOIUrl":"https://doi.org/arxiv-2409.07915","url":null,"abstract":"Splitting invariants are effective for distinguishing the embedded topology\u0000of plane curves. In this note, we introduce a generalization of splitting\u0000invariants, called the G-combinatorial type, for plane curves by using the\u0000modified plumbing graph defined by Hironaka [14]. We prove that the\u0000G-combinatorial type is invariant under certain homeomorphisms based on the\u0000arguments of Waldhausen [32, 33] and Neumann [22]. Furthermore, we distinguish\u0000the embedded topology of quasi-triangular curves by the G-combinatorial type,\u0000which are generalization of triangular curves studied in [4].","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Bruce-Roberts Numbers of 1-Forms on an ICIS","authors":"Bárbara K. Lima-Pereira, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto, João Nivaldo Tomazella","doi":"arxiv-2409.08380","DOIUrl":"https://doi.org/arxiv-2409.08380","url":null,"abstract":"We relate the Bruce-Roberts numbers of a 1-form with respect to an ICIS to\u0000other invariants as the GSV-index, Tjurina and Milnor numbers.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Amanda S. Araújo, Thaís M. Dalbelo, Thiago da Silva
In this work, we extend Saia's results on the characterization of Newton non-degenerate ideals to the context of ideals in $O_{X(S)}$, where $X(S)$ is an affine toric variety defined by the semigroup $Ssubset mathbb{Z}^{n}_{+}$. We explore the relationship between the integral closure of ideals and the Newton polyhedron. We introduce and characterize non-degenerate ideals, showing that their integral closure is generated by specific monomials related to the Newton polyhedron.
{"title":"Newton polyhedra and the integral closure of ideals on toric varieties","authors":"Amanda S. Araújo, Thaís M. Dalbelo, Thiago da Silva","doi":"arxiv-2409.07986","DOIUrl":"https://doi.org/arxiv-2409.07986","url":null,"abstract":"In this work, we extend Saia's results on the characterization of Newton\u0000non-degenerate ideals to the context of ideals in $O_{X(S)}$, where $X(S)$ is\u0000an affine toric variety defined by the semigroup $Ssubset mathbb{Z}^{n}_{+}$.\u0000We explore the relationship between the integral closure of ideals and the\u0000Newton polyhedron. We introduce and characterize non-degenerate ideals, showing\u0000that their integral closure is generated by specific monomials related to the\u0000Newton polyhedron.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli
A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations between polylogarithms rely on identities for those integration kernels. In this article, we derive identities for Enriquez' meromorphic generating function and investigate the implications for the associated integration kernels. The resulting identities are shown to be exhaustive and therefore reproduce all identities for Enriquez' kernels conjectured in arXiv:2407.11476 recently.
{"title":"Higher-genus Fay-like identities from meromorphic generating functions","authors":"Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli","doi":"arxiv-2409.08208","DOIUrl":"https://doi.org/arxiv-2409.08208","url":null,"abstract":"A possible way of constructing polylogarithms on Riemann surfaces of higher\u0000genera facilitates integration kernels, which can be derived from generating\u0000functions incorporating the geometry of the surface. Functional relations\u0000between polylogarithms rely on identities for those integration kernels. In\u0000this article, we derive identities for Enriquez' meromorphic generating\u0000function and investigate the implications for the associated integration\u0000kernels. The resulting identities are shown to be exhaustive and therefore\u0000reproduce all identities for Enriquez' kernels conjectured in arXiv:2407.11476\u0000recently.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop an equivariant version of the Pfaffian-Grassmannian correspondence and apply it to produce examples of nontrivial twisted equivariant stable birationalities between cubic threefolds and degree 14 Fano threefolds.
{"title":"Stable equivariant birationalities of cubic and degree 14 Fano threefolds","authors":"Yuri Tschinkel, Zhijia Zhang","doi":"arxiv-2409.08392","DOIUrl":"https://doi.org/arxiv-2409.08392","url":null,"abstract":"We develop an equivariant version of the Pfaffian-Grassmannian correspondence\u0000and apply it to produce examples of nontrivial twisted equivariant stable\u0000birationalities between cubic threefolds and degree 14 Fano threefolds.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show Kawamata's effective nonvanishing conjecture (also known as the Ambro--Kawamata nonvanishing conjecture) holds for quasismooth weighted complete intersections of codimension $2$. Namely, for a quasismooth weighted complete intersection $X$ of codimension $2$ and an ample Cartier divisor $H$ on $X$ such that $H-K_X$ is ample, the linear system $|H|$ is nonempty.
{"title":"Effective nonvanishing for weighted complete intersections of codimension two","authors":"Chen Jiang, Puyang Yu","doi":"arxiv-2409.07828","DOIUrl":"https://doi.org/arxiv-2409.07828","url":null,"abstract":"We show Kawamata's effective nonvanishing conjecture (also known as the\u0000Ambro--Kawamata nonvanishing conjecture) holds for quasismooth weighted\u0000complete intersections of codimension $2$. Namely, for a quasismooth weighted\u0000complete intersection $X$ of codimension $2$ and an ample Cartier divisor $H$\u0000on $X$ such that $H-K_X$ is ample, the linear system $|H|$ is nonempty.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The algebra of symmetric tensors $S(X):= H^0(X, sf{S}^{bullet} T_X)$ of a projective manifold $X$ leads to a natural dominant affinization morphism $$ varphi_X: T^*X longrightarrow mathcal{Z}_X:= text{Spec} S(X). $$ It is shown that $varphi_X$ is birational if and only if $T_X$ is big. We prove that if $varphi_X$ is birational, then $mathcal{Z}_X$ is a symplectic variety endowed with the Schouten--Nijenhuis bracket if and only if $mathbb{P} T_X$ is of Fano type, which is the case for smooth projective toric varieties, smooth horospherical varieties with small boundary and the quintic del Pezzo threefold. These give examples of a distinguished class of conical symplectic varieties, which we call symplectic orbifold cones.
{"title":"Symplectic singularities arising from algebras of symmetric tensors","authors":"Baohua Fu, Jie Liu","doi":"arxiv-2409.07264","DOIUrl":"https://doi.org/arxiv-2409.07264","url":null,"abstract":"The algebra of symmetric tensors $S(X):= H^0(X, sf{S}^{bullet} T_X)$ of a\u0000projective manifold $X$ leads to a natural dominant affinization morphism $$ varphi_X: T^*X longrightarrow mathcal{Z}_X:= text{Spec} S(X). $$ It is shown that $varphi_X$ is birational if and only if $T_X$ is big. We\u0000prove that if $varphi_X$ is birational, then $mathcal{Z}_X$ is a symplectic\u0000variety endowed with the Schouten--Nijenhuis bracket if and only if $mathbb{P}\u0000T_X$ is of Fano type, which is the case for smooth projective toric varieties,\u0000smooth horospherical varieties with small boundary and the quintic del Pezzo\u0000threefold. These give examples of a distinguished class of conical symplectic\u0000varieties, which we call symplectic orbifold cones.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we show a strange duality isomorphism at level one for the space of generalized theta functions on the moduli spaces of alternating anti-invariant vector bundles in the ramified case. These anti-invariant vector bundles constitute one of the non-trivial examples of parahoric G-torsors, where G is a twisted (not generically split) parahoric group scheme.
{"title":"Strange duality at level one for alternating vector bundles","authors":"Hacen Zelaci","doi":"arxiv-2409.07303","DOIUrl":"https://doi.org/arxiv-2409.07303","url":null,"abstract":"In this paper, we show a strange duality isomorphism at level one for the\u0000space of generalized theta functions on the moduli spaces of alternating\u0000anti-invariant vector bundles in the ramified case. These anti-invariant vector\u0000bundles constitute one of the non-trivial examples of parahoric G-torsors,\u0000where G is a twisted (not generically split) parahoric group scheme.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Justin Campbell, Lin Chen, Joakim Faergeman, Dennis Gaitsgory, Kevin Lin, Sam Raskin, Nick Rozenblyum
We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eisenstein-generated subcategories.
{"title":"Proof of the geometric Langlands conjecture III: compatibility with parabolic induction","authors":"Justin Campbell, Lin Chen, Joakim Faergeman, Dennis Gaitsgory, Kevin Lin, Sam Raskin, Nick Rozenblyum","doi":"arxiv-2409.07051","DOIUrl":"https://doi.org/arxiv-2409.07051","url":null,"abstract":"We establish the compatibility of the Langlands functor with the operations\u0000of Eisenstein series constant term, and deduce that the Langlands functor\u0000induces an equivalence on Eisenstein-generated subcategories.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"286 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is obtained. Second, a refinement of a result of Bujalance, Cirre, Gamboa and Gromadzki about signature realization is provided. Finally, we apply our results to isogeny decompositions of Jacobians by Prym varieties and by elliptic curves, extending results of Carocca, Recillas and Rodr'iguez. In particular, we give a complete classification of Jacobians with dihedral action whose group algebra decomposition induces a decomposition into factors of the same dimension.
{"title":"On Dihedral Group Actions on Riemann Surfaces","authors":"Pablo Alvarado-Seguel, Sebastián Reyes-Carocca","doi":"arxiv-2409.07294","DOIUrl":"https://doi.org/arxiv-2409.07294","url":null,"abstract":"This article deals with dihedral group actions on compact Riemann surfaces\u0000and the interplay between different geometric data associated to them. First, a\u0000bijective correspondence between geometric signatures and analytic\u0000representations is obtained. Second, a refinement of a result of Bujalance,\u0000Cirre, Gamboa and Gromadzki about signature realization is provided. Finally,\u0000we apply our results to isogeny decompositions of Jacobians by Prym varieties\u0000and by elliptic curves, extending results of Carocca, Recillas and Rodr'iguez.\u0000In particular, we give a complete classification of Jacobians with dihedral\u0000action whose group algebra decomposition induces a decomposition into factors\u0000of the same dimension.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：