{"title":"Les squelettes accessibles d'un espace de Berkovich","authors":"Antoine Ducros, Amaury Thuillier","doi":"arxiv-2409.08755","DOIUrl":"https://doi.org/arxiv-2409.08755","url":null,"abstract":"We define a class of skeletons on Berkovich analytic spaces, which we call\u0000\"accessible\", which contains the standard skeleton of the n-dimensional torus\u0000for every n and is preserved by G-glueing, by taking the inverse image along a\u0000morphism of relative dimension zero, and by taking the direct image along a\u0000morphism whose restriction to the involved skeleton is topologically proper.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253203","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}
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco
{"title":"Nonnegativity certificates on real algebraic surfaces","authors":"Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco","doi":"arxiv-2409.08834","DOIUrl":"https://doi.org/arxiv-2409.08834","url":null,"abstract":"We introduce tools for transferring nonnegativity certificates for global\u0000sections between line bundles on real algebraic surfaces. As applications, we\u0000improve Hilbert's degree bounds on sum-of-squares multipliers for nonnegative\u0000ternary forms, give a complete characterization of nonnegative real forms of\u0000del Pezzo surfaces, and establish quadratic upper bounds for the degrees of\u0000sum-of-squares multipliers for nonnegative forms on real ruled surfaces.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253169","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}
D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum
{"title":"Proof of the geometric Langlands conjecture IV: ambidexterity","authors":"D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum","doi":"arxiv-2409.08670","DOIUrl":"https://doi.org/arxiv-2409.08670","url":null,"abstract":"This paper performs the following steps toward the proof of GLC in the de\u0000Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [GLC1], when\u0000restricted to the cuspidal category, is ambidextrous; (iii) We reduce GLC to the study of a certain classical vector bundle with\u0000connection on the stack of irreducible local systems; (iv) We prove that GLC is equivalent to the contractibility of the space of\u0000generic oper structures on irreducible local systems; (v) Using [BKS], we deduce GLC for classical groups.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253170","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":"A smooth but non-symplectic moduli of sheaves on a hyperkähler variety","authors":"Andreas Krug, Fabian Reede, Ziyu Zhang","doi":"arxiv-2409.08991","DOIUrl":"https://doi.org/arxiv-2409.08991","url":null,"abstract":"For an abelian surface $A$, we consider stable vector bundles on a\u0000generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected\u0000component of the moduli space which contains the tautological bundles\u0000associated to line bundles of degree $0$ is isomorphic to the blowup of the\u0000dual abelian surface in one point. We believe that this is the first explicit\u0000example of a component which is smooth with a non-trivial canonical bundle.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253167","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":"Faber--Pandharipande Cycles vanish for Shimura curves","authors":"Congling Qiu","doi":"arxiv-2409.08989","DOIUrl":"https://doi.org/arxiv-2409.08989","url":null,"abstract":"A result of Green and Griffiths states that for the generic curve $C$ of\u0000genus $g geq 4$ with the canonical divisor $K$, its Faber--Pandharipande\u00000-cycle $Ktimes K-(2g-2)K_Delta$ on $Ctimes C$ is nontorsion in the Chow\u0000group of rational equivalence classes. For Shimura curves, however, we show\u0000that their Faber--Pandharipande 0-cycles are rationally equivalent to 0. This\u0000is predicted by a conjecture of Beilinson and Bloch.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"192 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253168","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":"Rationality of Brauer-Severi surface bundles over rational 3-folds","authors":"Shitan Xu","doi":"arxiv-2409.08504","DOIUrl":"https://doi.org/arxiv-2409.08504","url":null,"abstract":"We give a sufficient condition for a Brauer-Severi surface bundle over a\u0000rational 3-fold to not be stably rational. Additionally, we present an example\u0000that satisfies this condition and demonstrate the existence of families of\u0000Brauer-Severi surface bundles whose general members are smooth and not stably\u0000rational.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253171","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":"Cubic fourfolds with symplectic automorphisms","authors":"Kenji Koike","doi":"arxiv-2409.08448","DOIUrl":"https://doi.org/arxiv-2409.08448","url":null,"abstract":"We determine projective equations of smooth complex cubic fourfolds with\u0000symplectic automorphisms by classifying 6-dimensional projective\u0000representations of Laza and Zheng's 34 groups. In particular, we determine the\u0000number of irreducible components for moduli spaces of cubic fourfolds with\u0000symplectic actions by these groups. We also discuss the fields of definition of\u0000cubic fourfolds in six maximal cases.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253172","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":"Logarithmic Enriques varieties","authors":"Samuel Boissiere, Chiara Camere, Alessandra Sarti","doi":"arxiv-2409.09160","DOIUrl":"https://doi.org/arxiv-2409.09160","url":null,"abstract":"We introduce logarithmic Enriques varieties as a singular analogue of\u0000Enriques manifolds, generalizing the notion of log-Enriques surfaces introduced\u0000by Zhang. We focus then on the properties of the subfamily of log-Enriques\u0000varieties that admit a quasi-'etale cover by a singular symplectic variety and\u0000we give many examples.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253097","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}
Andriy Regeta, Christian Urech, Immanuel van Santen
{"title":"Group Theoretical Characterizations of Rationality","authors":"Andriy Regeta, Christian Urech, Immanuel van Santen","doi":"arxiv-2409.07864","DOIUrl":"https://doi.org/arxiv-2409.07864","url":null,"abstract":"Let X be an irreducible variety and Bir(X) its group of birational\u0000transformations. We show that the group structure of Bir(X) determines whether\u0000X is rational and whether X is ruled. Additionally, we prove that any Borel subgroup of Bir(X) has derived length\u0000at most twice the dimension of X, with equality occurring if and only if X is\u0000rational and the Borel subgroup is standard. We also provide examples of\u0000non-standard Borel subgroups of Bir(P^n) and Aut(A^n), thereby resolving\u0000conjectures by Popov and Furter-Poloni.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220342","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}
Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske
{"title":"2-Gorenstein stable surfaces with $K_X^2 = 1$ and $χ(X) = 3$","authors":"Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske","doi":"arxiv-2409.07854","DOIUrl":"https://doi.org/arxiv-2409.07854","url":null,"abstract":"The compactification $overline M_{1,3}$ of the Gieseker moduli space of\u0000surfaces of general type with $K_X^2 =1 $ and $chi(X)=3$ in the moduli space\u0000of stable surfaces parametrises so-called stable I-surfaces. We classify all such surfaces which are 2-Gorenstein into four types using a\u0000mix of algebraic and geometric techniques. We find a new divisor in the closure\u0000of the Gieseker component and a new irreducible component of the moduli space.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220341","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}
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