{"title":"Examples of surfaces with canonical map of degree 4","authors":"Carlos Rito","doi":"10.46298/epiga.2022.7615","DOIUrl":"https://doi.org/10.46298/epiga.2022.7615","url":null,"abstract":"We give two examples of surfaces with canonical map of degree 4 onto a\u0000canonical surface.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48856675","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":"Chern currents of coherent sheaves","authors":"Richard Larkang, Elizabeth Wulcan","doi":"10.46298/epiga.2022.8653","DOIUrl":"https://doi.org/10.46298/epiga.2022.8653","url":null,"abstract":"Given a finite locally free resolution of a coherent analytic sheaf $mathcal\u0000F$, equipped with Hermitian metrics and connections, we construct an explicit\u0000current, obtained as the limit of certain smooth Chern forms of $mathcal F$,\u0000that represents the Chern class of $mathcal F$ and has support on the support\u0000of $mathcal F$. If the connections are $(1,0)$-connections and $mathcal F$\u0000has pure dimension, then the first nontrivial component of this Chern current\u0000coincides with (a constant times) the fundamental cycle of $mathcal F$. The\u0000proof of this goes through a generalized Poincar'e-Lelong formula, previously\u0000obtained by the authors, and a result that relates the Chern current to the\u0000residue current associated with the locally free resolution.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484270","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":"N'eron models of Jacobians over bases of arbitrary dimension","authors":"Thibault Poiret","doi":"10.46298/epiga.2022.7340","DOIUrl":"https://doi.org/10.46298/epiga.2022.7340","url":null,"abstract":"We work with a smooth relative curve $X_U/U$ with nodal reduction over an\u0000excellent and locally factorial scheme $S$. We show that blowing up a nodal\u0000model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and\u0000describe how these models relate to each other. We construct a N'eron model\u0000for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the\u0000Picard space of a well-chosen nodal model. We provide a combinatorial criterion\u0000for the N'eron model to be separated.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484156","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":"'Etale triviality of finite equivariant vector bundles","authors":"I. Biswas, P. O'Sullivan","doi":"10.46298/epiga.2021.7275","DOIUrl":"https://doi.org/10.46298/epiga.2021.7275","url":null,"abstract":"Let H be a complex Lie group acting holomorphically on a complex analytic\u0000space X such that the restriction to X_{mathrm{red}} of every H-invariant\u0000regular function on X is constant. We prove that an H-equivariant holomorphic\u0000vector bundle E over X is $H$-finite, meaning f_1(E)= f_2(E) as H-equivariant\u0000bundles for two distinct polynomials f_1 and f_2 whose coefficients are\u0000nonnegative integers, if and only if the pullback of E along some H-equivariant\u0000finite 'etale covering of X is trivial as an H-equivariant bundle.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484519","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 conjectures of Artin-Tate and Birch-Swinnerton-Dyer","authors":"S. Lichtenbaum, N. Ramachandran, T. Suzuki","doi":"10.46298/epiga.2022.7482","DOIUrl":"https://doi.org/10.46298/epiga.2022.7482","url":null,"abstract":"We provide two proofs that the conjecture of Artin-Tate for a fibered surface\u0000is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of\u0000the generic fibre. As a byproduct, we obtain a new proof of a theorem of\u0000Geisser relating the orders of the Brauer group and the Tate-Shafarevich group.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49348119","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":"Moduli spaces of stable sheaves over quasi-polarized surfaces, and the\u0000 relative Strange Duality morphism","authors":"Svetlana A. Makarova","doi":"10.46298/epiga.2021.7174","DOIUrl":"https://doi.org/10.46298/epiga.2021.7174","url":null,"abstract":"The main result of the present paper is a construction of relative moduli\u0000spaces of stable sheaves over the stack of quasipolarized projective surfaces.\u0000For this, we use the theory of good moduli spaces, whose study was initiated by\u0000Alper. As a corollary, we extend the relative Strange Duality morphism to the\u0000locus of quasipolarized K3 surfaces.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484482","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}