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The Structure of Algebraic Families of Birational Transformations 双向变换代数族的结构
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-10 DOI: arxiv-2409.06475
Andriy Regeta, Christian Urech, Immanuel van Santen
{"title":"The Structure of Algebraic Families of Birational Transformations","authors":"Andriy Regeta, Christian Urech, Immanuel van Santen","doi":"arxiv-2409.06475","DOIUrl":"https://doi.org/arxiv-2409.06475","url":null,"abstract":"We give a description of the algebraic families of birational transformations\u0000of an algebraic variety X. As an application, we show that the morphisms to\u0000Bir(X) given by algebraic families satisfy a Chevalley type result and a\u0000certain fibre-dimension formula. Moreover, we show that the algebraic subgroups\u0000of Bir(X) are exactly the closed finite-dimensional subgroups with finitely\u0000many components. We also study algebraic families of birational transformations\u0000preserving a fibration. This builds on previous work of Blanc-Furter, Hanamura,\u0000and Ramanujam.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220349","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
Infinitesimal deformations of some quot schemes, II 一些 quot 方案的微小变形，II
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-10 DOI: arxiv-2409.06434
Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian
{"title":"Infinitesimal deformations of some quot schemes, II","authors":"Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian","doi":"arxiv-2409.06434","DOIUrl":"https://doi.org/arxiv-2409.06434","url":null,"abstract":"Let $C$ be an irreducible smooth complex projective curve of genus $g$, with\u0000$g_C geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$, with\u0000$rgeqslant 2$. Let $mc Q:=mc Q(E,,d)$ be the Quot Scheme parameterizing\u0000torsion quotients of $E$ of degree $d$. We explicitly describe all deformations\u0000of $mc Q$.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227411","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
Varieties with two smooth blow up structures 具有两个平滑吹胀结构的品种
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-10 DOI: arxiv-2409.10560
Supravat Sarkar
{"title":"Varieties with two smooth blow up structures","authors":"Supravat Sarkar","doi":"arxiv-2409.10560","DOIUrl":"https://doi.org/arxiv-2409.10560","url":null,"abstract":"We classify smooth projective varieties of Picard rank 2 which has two\u0000structures of blow-up of projective space along smooth subvarieties of\u0000different dimensions. This gives a characterization of the so called\u0000quadro-cubic Cremona transformation.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253205","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
Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks 加权投影堆栈中非凸完全相交的格罗莫夫--维滕不变式
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-10 DOI: arxiv-2409.06193
Felix Janda, Nawaz Sultani, Yang Zhou
{"title":"Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks","authors":"Felix Janda, Nawaz Sultani, Yang Zhou","doi":"arxiv-2409.06193","DOIUrl":"https://doi.org/arxiv-2409.06193","url":null,"abstract":"In this paper we compute genus 0 orbifold Gromov--Witten invariants of\u0000Calabi--Yau threefold complete intersections in weighted projective stacks,\u0000regardless of convexity conditions. The traditional quantumn Lefschetz\u0000principle may fail even for invariants with ambient insertions. Using quasimap\u0000wall-crossing, we are able to compute invariants with insertions from a\u0000specific subring of the Chen--Ruan cohomology, which contains all the ambient\u0000cohomology classes. Quasimap wall-crossing gives a mirror theorem expressing the I-function in\u0000terms of the J-function via a mirror map. The key of this paper is to find a\u0000suitable GIT presentation of the target space, so that the mirror map is\u0000invertible. An explicit formula for the I-function is given for all those\u0000target spaces and many examples with explicit computations of invariants are\u0000provided.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220374","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
Moduli of Anti-Invariant Higgs Bundles 反不变希格斯束的模量
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-09 DOI: arxiv-2409.05793
Karim Réga
{"title":"Moduli of Anti-Invariant Higgs Bundles","authors":"Karim Réga","doi":"arxiv-2409.05793","DOIUrl":"https://doi.org/arxiv-2409.05793","url":null,"abstract":"We study the moduli of anti-invariant Higgs bundles as introduced by Zelaci.\u0000Using recent existence results of Alper, Halpern-Leistner and Heinloth we\u0000establish the existence of a separated good moduli space for semistable\u0000anti-invariant Higgs bundles. Along the way this produces a non-GIT proof of\u0000the existence of a separated good moduli space for semistable Higgs bundles. We\u0000also prove the properness of the Hitchin system in this setting.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220375","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
Fibrations by plane projective rational quartic curves in characteristic two 特征二中平面射影有理四边形曲线的纤度
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-09 DOI: arxiv-2409.05464
Cesar Hilario, Karl-Otto Stöhr
{"title":"Fibrations by plane projective rational quartic curves in characteristic two","authors":"Cesar Hilario, Karl-Otto Stöhr","doi":"arxiv-2409.05464","DOIUrl":"https://doi.org/arxiv-2409.05464","url":null,"abstract":"We give a complete classification, up to birational equivalence, of all\u0000fibrations by plane projective rational quartic curves in characteristic two.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227412","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
Parahoric reduction theory of formal connections (or Higgs fields) 形式连接（或希格斯场）的准还原理论
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05073
Zhi Hu, Pengfei Huang, Ruiran Sun, Runhong Zong
{"title":"Parahoric reduction theory of formal connections (or Higgs fields)","authors":"Zhi Hu, Pengfei Huang, Ruiran Sun, Runhong Zong","doi":"arxiv-2409.05073","DOIUrl":"https://doi.org/arxiv-2409.05073","url":null,"abstract":"In this paper, we establish the parahoric reduction theory of formal\u0000connections (or Higgs fields) on a formal principal bundle with parahoric\u0000structures, which generalizes Babbitt-Varadarajan's result for the case without\u0000parahoric structures [5] and Boalch's result for the case of regular\u0000singularity [9]. As applications, we prove the equivalence between extrinsic\u0000definition and intrinsic definition of regular singularity and provide a\u0000criterion of relative regularity for formal connections, and also demonstrate a\u0000parahoric version of Frenkel-Zhu's Borel reduction theorem of formal\u0000connections [23].","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220436","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
Transverse-freeness in finite geometries 有限几何中的横向自由度
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05248
Charlie Bruggemann, Vera Choi, Brian Freidin, Jaedon Whyte
{"title":"Transverse-freeness in finite geometries","authors":"Charlie Bruggemann, Vera Choi, Brian Freidin, Jaedon Whyte","doi":"arxiv-2409.05248","DOIUrl":"https://doi.org/arxiv-2409.05248","url":null,"abstract":"We study projective curves and hypersurfaces defined over a finite field that\u0000are tangent to every member of a class of low-degree varieties. Extending\u00002-dimensional work of Asgarli, we first explore the lowest degrees attainable\u0000by smooth hypersurfaces in $n$-dimensional projective space that are tangent to\u0000every $k$-dimensional subspace, for some value of $n$ and $k$. We then study\u0000projective surfaces that serve as models of finite inversive and hyperbolic\u0000planes, finite analogs of spherical and hyperbolic geometries. In these\u0000surfaces we construct curves tangent to each of the lowest degree curves\u0000defined over the base field.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220376","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
Extremal Contraction of Projective Bundles 射影束的极值收缩
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-08 DOI: arxiv-2409.05091
Ashima Bansal, Supravat Sarkar, Shivam Vats
{"title":"Extremal Contraction of Projective Bundles","authors":"Ashima Bansal, Supravat Sarkar, Shivam Vats","doi":"arxiv-2409.05091","DOIUrl":"https://doi.org/arxiv-2409.05091","url":null,"abstract":"In this article, we explore the extremal contractions of several projective\u0000bundles over smooth Fano varieties of Picard rank $1$. We provide a whole class\u0000of examples of projective bundles with smooth blow-up structures, derived from\u0000the notion of drums which was introduced by Occhetta-Romano-Conde-Wi'sniewski\u0000to study interaction with $mathbb{C}^*$-actions and birational geometry. By\u0000manipulating projective bundles, we give a simple geometric construction of the\u0000rooftop flip, which was introduced recently by Barban-Franceschini.\u0000Additionally, we obtain analogues of some recent results of Vats in higher\u0000dimensions. The list of projective bundles we consider includes all globally\u0000generated bundles over projective space with first Chern class $2$. For each of\u0000them, we compute the nef and pseudoeffective cones.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220377","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
Nash blowups of 2-generic determinantal varieties in positive characteristic 正特征中二属行列式变种的纳什炸裂
arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-07 DOI: arxiv-2409.04688
Thaís M. Dalbelo, Daniel Duarte, Maria Aparecida Soares Ruas
{"title":"Nash blowups of 2-generic determinantal varieties in positive characteristic","authors":"Thaís M. Dalbelo, Daniel Duarte, Maria Aparecida Soares Ruas","doi":"arxiv-2409.04688","DOIUrl":"https://doi.org/arxiv-2409.04688","url":null,"abstract":"We show that the Nash blowup of 2-generic determinantal varieties over fields\u0000of positive characteristic is non-singular. We prove this in two steps.\u0000Firstly, we explicitly describe the toric structure of such varieties.\u0000Secondly, we show that in this case the combinatorics of Nash blowups are free\u0000of characteristic. The result then follows from the analogous result in\u0000characteristic zero proved by W. Ebeling and S. M. Gusein-Zade.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220380","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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