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A note on combinatorial type and splitting invariants of plane curves 关于平面曲线的组合类型和分裂不变式的说明
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.07915
Taketo Shirane
{"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":null,"pages":null},"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}
引用次数: 0
The Bruce-Roberts Numbers of 1-Forms on an ICIS ICIS 上的布鲁斯-罗伯茨一元数
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.08380
Bárbara K. Lima-Pereira, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto, João Nivaldo Tomazella
{"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":null,"pages":null},"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}
引用次数: 0
Newton polyhedra and the integral closure of ideals on toric varieties 牛顿多面体与环状变体上理想的积分闭合
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.07986
Amanda S. Araújo, Thaís M. Dalbelo, Thiago da Silva
{"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":null,"pages":null},"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}
引用次数: 0
Higher-genus Fay-like identities from meromorphic generating functions 来自分形生成函数的高属法伊同分异构体
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.08208
Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli
{"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":null,"pages":null},"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}
引用次数: 0
Stable equivariant birationalities of cubic and degree 14 Fano threefolds 立方和 14 度 Fano 三折的稳定等变性
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.08392
Yuri Tschinkel, Zhijia Zhang
{"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":null,"pages":null},"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}
引用次数: 0
Effective nonvanishing for weighted complete intersections of codimension two 二维加权完全交叉的有效非消失
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI: arxiv-2409.07828
Chen Jiang, Puyang Yu
{"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":null,"pages":null},"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}
引用次数: 0
Symplectic singularities arising from algebras of symmetric tensors 由对称张量代数引起的交映奇点
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-11 DOI: arxiv-2409.07264
Baohua Fu, Jie Liu
{"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":null,"pages":null},"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}
引用次数: 0
Strange duality at level one for alternating vector bundles 交替向量束第一级的奇异对偶性
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-11 DOI: arxiv-2409.07303
Hacen Zelaci
{"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":null,"pages":null},"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}
引用次数: 0
Proof of the geometric Langlands conjecture III: compatibility with parabolic induction 几何朗兰兹猜想 III 的证明：与抛物线归纳法的兼容性
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-11 DOI: arxiv-2409.07051
Justin Campbell, Lin Chen, Joakim Faergeman, Dennis Gaitsgory, Kevin Lin, Sam Raskin, Nick Rozenblyum
{"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":null,"pages":null},"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}
引用次数: 0
On Dihedral Group Actions on Riemann Surfaces 论黎曼曲面上的二面群作用
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-11 DOI: arxiv-2409.07294
Pablo Alvarado-Seguel, Sebastián Reyes-Carocca
{"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":null,"pages":null},"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}
引用次数: 0
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