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Epijournal de Geometrie Algebrique最新文献

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Examples of surfaces with canonical map of degree 4 具有4次正则映射的曲面的例子
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-06-06 DOI: 10.46298/epiga.2022.7615
Carlos Rito
{"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}
引用次数: 2
Chern currents of coherent sheaves 相干捆的陈氏电流
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-05-31 DOI: 10.46298/epiga.2022.8653
Richard Larkang, Elizabeth Wulcan
{"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}
引用次数: 1
N'eron models of Jacobians over bases of arbitrary dimension 任意维基上雅可比矩阵的N 'eron模型
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-03-11 DOI: 10.46298/epiga.2022.7340
Thibault Poiret
{"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}
引用次数: 1
'Etale triviality of finite equivariant vector bundles 有限等变向量束的一般平凡性
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-03-11 DOI: 10.46298/epiga.2021.7275
I. Biswas, P. O'Sullivan
{"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}
引用次数: 1
The conjectures of Artin-Tate and Birch-Swinnerton-Dyer Artin Tate和Birch Swinnerton Dyer的猜想
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-01-25 DOI: 10.46298/epiga.2022.7482
S. Lichtenbaum, N. Ramachandran, T. Suzuki
{"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}
引用次数: 2
Moduli spaces of stable sheaves over quasi-polarized surfaces, and the relative Strange Duality morphism 准极化表面上稳定束的模空间及相对奇异对偶态射
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2021-01-01 DOI: 10.46298/epiga.2021.7174
Svetlana A. Makarova
{"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}
引用次数: 1
Factorization of the Abel-Jacobi maps Abel-Jacobi映射的因子分解
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-12-09 DOI: 10.46298/epiga.2021.6969
Fumiaki Suzuki
{"title":"Factorization of the Abel-Jacobi maps","authors":"Fumiaki Suzuki","doi":"10.46298/epiga.2021.6969","DOIUrl":"https://doi.org/10.46298/epiga.2021.6969","url":null,"abstract":"As an application of the theory of Lawson homology and morphic cohomology,\u0000Walker proved that the Abel-Jacobi map factors through another regular\u0000homomorphism. In this note, we give a direct proof of the theorem.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484297","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: 4
Stably semiorthogonally indecomposable varieties 稳定的半正交不可分解品种
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-11-25 DOI: 10.46298/epiga.2023.volume7.7700
D. Pirozhkov
{"title":"Stably semiorthogonally indecomposable varieties","authors":"D. Pirozhkov","doi":"10.46298/epiga.2023.volume7.7700","DOIUrl":"https://doi.org/10.46298/epiga.2023.volume7.7700","url":null,"abstract":"A triangulated category is said to be indecomposable if it admits no\u0000nontrivial semiorthogonal decompositions. We introduce a definition of a\u0000noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This\u0000propery implies, among other things, that each smooth proper subvariety has\u0000indecomposable derived category of coherent sheaves, and that if $Y$ is NSSI,\u0000then for any variety $X$ all semiorthogonal decompositions of $X times Y$ are\u0000induced from decompositions of $X$. We prove that any variety whose Albanese\u0000morphism is finite is NSSI, and that the total space of a fibration over NSSI\u0000base with NSSI fibers is also NSSI. We apply this indecomposability to deduce\u0000that there are no phantom subcategories in some varieties, including surfaces\u0000$C times mathbb{P}^1$, where $C$ is any smooth proper curve of positive\u0000genus.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485285","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: 7
Non-Archimedean volumes of metrized nef line bundles 公制网束的非阿基米德体积
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-11-13 DOI: 10.46298/epiga.2021.6908
S. Boucksom, Walter Gubler, Florent Martin
{"title":"Non-Archimedean volumes of metrized nef line bundles","authors":"S. Boucksom, Walter Gubler, Florent Martin","doi":"10.46298/epiga.2021.6908","DOIUrl":"https://doi.org/10.46298/epiga.2021.6908","url":null,"abstract":"Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a\u0000non-trivially valued non-Archimedean field $K$. Roughly speaking, the\u0000non-Archimedean volume of a continuous metric on the Berkovich analytification\u0000of $L$ measures the asymptotic growth of the space of small sections of tensor\u0000powers of $L$. For a continuous semipositive metric on $L$ in the sense of\u0000Zhang, we show first that the non-Archimedean volume agrees with the energy.\u0000The existence of such a semipositive metric yields that $L$ is nef. A second\u0000result is that the non-Archimedean volume is differentiable at any semipositive\u0000continuous metric. These results are known when $L$ is ample, and the purpose\u0000of this paper is to generalize them to the nef case. The method is based on a\u0000detailed study of the content and the volume of a finitely presented torsion\u0000module over the (possibly non-noetherian) valuation ring of $K$.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484214","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: 5
Quartic surface, its bitangents and rational points 四次曲面及其切点和有理点
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-10-16 DOI: 10.46298/epiga.2022.8987
P. Corvaja, F. Zucconi
{"title":"Quartic surface, its bitangents and rational points","authors":"P. Corvaja, F. Zucconi","doi":"10.46298/epiga.2022.8987","DOIUrl":"https://doi.org/10.46298/epiga.2022.8987","url":null,"abstract":"Let X be a smooth quartic surface not containing lines, defined over a number\u0000field K. We prove that there are only finitely many bitangents to X which are\u0000defined over K. This result can be interpreted as saying that a certain\u0000surface, having vanishing irregularity, contains only finitely many rational\u0000points. In our proof, we use the geometry of lines of the quartic double solid\u0000associated to X. In a somewhat opposite direction, we show that on any quartic\u0000surface X over a number field K, the set of algebraic points in X(overeline K)\u0000which are quadratic over a suitable finite extension K' of K is Zariski-dense.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484453","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: 1
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