Pub Date : 2021-11-18DOI: 10.46298/epiga.2023.8734
Pascal Fong
We classify the maximal algebraic subgroups of Bir(CxPP^1), when C is a smooth projective curve of positive genus.
当C为正属光滑投影曲线时，我们对Bir(CxPP^1)的极大代数子群进行了分类。
{"title":"Algebraic subgroups of the group of birational transformations of ruled surfaces","authors":"Pascal Fong","doi":"10.46298/epiga.2023.8734","DOIUrl":"https://doi.org/10.46298/epiga.2023.8734","url":null,"abstract":"We classify the maximal algebraic subgroups of Bir(CxPP^1), when C is a\u0000smooth projective curve of positive genus.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485024","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}
Pub Date : 2021-10-20DOI: 10.46298/epiga.2023.volume7.8803
Quentin Posva
We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on abundance for lc surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon and Xu to descend semi-ampleness from the normalization. We also present applications to dlt threefold pairs, and to mixed characteristic families of surfaces.
{"title":"Abundance for slc surfaces over arbitrary fields","authors":"Quentin Posva","doi":"10.46298/epiga.2023.volume7.8803","DOIUrl":"https://doi.org/10.46298/epiga.2023.volume7.8803","url":null,"abstract":"We prove the abundance conjecture for projective slc surfaces over arbitrary\u0000fields of positive characteristic. The proof relies on abundance for lc\u0000surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon\u0000and Xu to descend semi-ampleness from the normalization. We also present\u0000applications to dlt threefold pairs, and to mixed characteristic families of\u0000surfaces.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485455","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}
Pub Date : 2021-09-30DOI: 10.46298/epiga.2022.8595
A. Buryak, Francisco Hernandez Iglesias, S. Shadrin
We propose a conjectural formula for $DR_g(a,-a) lambda_g$ and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu'er'e and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way.
{"title":"A conjectural formula for $DR_g(a,-a) lambda_g$","authors":"A. Buryak, Francisco Hernandez Iglesias, S. Shadrin","doi":"10.46298/epiga.2022.8595","DOIUrl":"https://doi.org/10.46298/epiga.2022.8595","url":null,"abstract":"We propose a conjectural formula for $DR_g(a,-a) lambda_g$ and check all its\u0000expected properties. Our formula refines the one point case of a similar\u0000conjecture made by the first named author in collaboration with Gu'er'e and\u0000Rossi, and we prove that the two conjectures are in fact equivalent, though in\u0000a quite non-trivial way.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484222","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}
Pub Date : 2021-09-28DOI: 10.46298/epiga.2022.9611
S. Feyzbakhsh, L. Pertusi
We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $text{GL}^+_2(mathbb{R})$. We apply this result to the Kuznetsov component $text{Ku}(X)$ of a cubic threefold $X$. In particular, we show that all the known stability conditions on $text{Ku}(X)$ are invariant with respect to the action of the Serre functor and thus lie in the same orbit with respect to the action of the universal cover of $text{GL}^+_2(mathbb{R})$. As an application, we show that the moduli space of Ulrich bundles of rank $geq 2$ on $X$ is irreducible, answering a question asked by Lahoz, Macr`i and Stellari.
{"title":"Serre-invariant stability conditions and Ulrich bundles on cubic threefolds","authors":"S. Feyzbakhsh, L. Pertusi","doi":"10.46298/epiga.2022.9611","DOIUrl":"https://doi.org/10.46298/epiga.2022.9611","url":null,"abstract":"We prove a general criterion which ensures that a fractional Calabi--Yau\u0000category of dimension $leq 2$ admits a unique Serre-invariant stability\u0000condition, up to the action of the universal cover of\u0000$text{GL}^+_2(mathbb{R})$. We apply this result to the Kuznetsov component\u0000$text{Ku}(X)$ of a cubic threefold $X$. In particular, we show that all the\u0000known stability conditions on $text{Ku}(X)$ are invariant with respect to the\u0000action of the Serre functor and thus lie in the same orbit with respect to the\u0000action of the universal cover of $text{GL}^+_2(mathbb{R})$. As an\u0000application, we show that the moduli space of Ulrich bundles of rank $geq 2$\u0000on $X$ is irreducible, answering a question asked by Lahoz, Macr`i and\u0000Stellari.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49556028","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}
Pub Date : 2021-08-17DOI: 10.46298/epiga.2023.9742
Tomoyuki Abe
The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D'{e}glise. We also construct an $infty$-enhancement of such a trace formalism. In the course of the $infty$-enhancement, we need to reinterpret the trace formalism in a more functorial manner. This is done by using Suslin-Voevodsky's relative cycle groups.
{"title":"Trace formalism for motivic cohomology","authors":"Tomoyuki Abe","doi":"10.46298/epiga.2023.9742","DOIUrl":"https://doi.org/10.46298/epiga.2023.9742","url":null,"abstract":"The goal of this paper is to construct trace maps for the six functor\u0000formalism of motivic cohomology after Voevodsky, Ayoub, and\u0000Cisinski-D'{e}glise. We also construct an $infty$-enhancement of such a trace\u0000formalism. In the course of the $infty$-enhancement, we need to reinterpret\u0000the trace formalism in a more functorial manner. This is done by using\u0000Suslin-Voevodsky's relative cycle groups.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485203","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}
Pub Date : 2021-08-11DOI: 10.46298/epiga.2023.volume7.8702
Kenneth Ascher, Dori Bejleri
Using log geometry, we study smoothability of genus zero twisted stable maps to stacky curves relative to a collection of marked points. One application is to smoothing semi-log canonical fibered surfaces with marked singular fibers.
{"title":"Smoothability of relative stable maps to stacky curves","authors":"Kenneth Ascher, Dori Bejleri","doi":"10.46298/epiga.2023.volume7.8702","DOIUrl":"https://doi.org/10.46298/epiga.2023.volume7.8702","url":null,"abstract":"Using log geometry, we study smoothability of genus zero twisted stable maps\u0000to stacky curves relative to a collection of marked points. One application is\u0000to smoothing semi-log canonical fibered surfaces with marked singular fibers.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485391","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}
Pub Date : 2021-08-10DOI: 10.46298/epiga.2022.8352
Margarida Melo, S. Molcho, Martin Ulirsch, Filippo Viviani
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.
{"title":"Tropicalization of the universal Jacobian","authors":"Margarida Melo, S. Molcho, Martin Ulirsch, Filippo Viviani","doi":"10.46298/epiga.2022.8352","DOIUrl":"https://doi.org/10.46298/epiga.2022.8352","url":null,"abstract":"In this article we provide a stack-theoretic framework to study the universal\u0000tropical Jacobian over the moduli space of tropical curves. We develop two\u0000approaches to the process of tropicalization of the universal compactified\u0000Jacobian over the moduli space of curves -- one from a logarithmic and the\u0000other from a non-Archimedean analytic point of view. The central result from\u0000both points of view is that the tropicalization of the universal compactified\u0000Jacobian is the universal tropical Jacobian and that the tropicalization maps\u0000in each of the two contexts are compatible with the tautological morphisms. In\u0000a sequel we will use the techniques developed here to provide explicit\u0000polyhedral models for the logarithmic Picard variety.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49317398","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}
Pub Date : 2021-07-25DOI: 10.46298/epiga.2022.volume6.8504
T. Koike, Takato Uehara
We construct a non-Kummer projective K3 surface $X$ which admits compact Levi-flats by holomorphically patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective plane at nine general points.
{"title":"A gluing construction of projective K3 surfaces","authors":"T. Koike, Takato Uehara","doi":"10.46298/epiga.2022.volume6.8504","DOIUrl":"https://doi.org/10.46298/epiga.2022.volume6.8504","url":null,"abstract":"We construct a non-Kummer projective K3 surface $X$ which admits compact\u0000Levi-flats by holomorphically patching two open complex surfaces obtained as\u0000the complements of tubular neighborhoods of elliptic curves embedded in\u0000blow-ups of the projective plane at nine general points.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484896","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}
Pub Date : 2021-06-26DOI: 10.46298/epiga.2022.volume6.7641
Beren Sanders
We provide a characterization of finite 'etale morphisms in tensor triangular geometry. They are precisely those functors which have a conservative right adjoint, satisfy Grothendieck--Neeman duality, and for which the relative dualizing object is trivial (via a canonically-defined map).
{"title":"A characterization of finite 'etale morphisms in tensor triangular geometry","authors":"Beren Sanders","doi":"10.46298/epiga.2022.volume6.7641","DOIUrl":"https://doi.org/10.46298/epiga.2022.volume6.7641","url":null,"abstract":"We provide a characterization of finite 'etale morphisms in tensor\u0000triangular geometry. They are precisely those functors which have a\u0000conservative right adjoint, satisfy Grothendieck--Neeman duality, and for which\u0000the relative dualizing object is trivial (via a canonically-defined map).","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484838","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}
Pub Date : 2021-06-23DOI: 10.46298/epiga.2021.7626
K. Hashizume
We prove the existence of a crepant sdlt model for slc pairs whose irreducible components are normal in codimension one.
我们证明了在余维1中可约分量为正规的slc对的creant sdlt模型的存在性。
{"title":"Crepant semi-divisorial log terminal model","authors":"K. Hashizume","doi":"10.46298/epiga.2021.7626","DOIUrl":"https://doi.org/10.46298/epiga.2021.7626","url":null,"abstract":"We prove the existence of a crepant sdlt model for slc pairs whose\u0000irreducible components are normal in codimension one.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48286167","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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