On the Schottky problem for genus-five Jacobians with a vanishing theta-null

被引：0

作者：

Agostini, Daniele ^{[1
]}

Chua, Lynn ^{[2
]}

机构：

[1] Max Planck Inst Math Nat Wissensch, Inselstr 4, D-04103 Leipzig, Germany

[2] CALTECH, Dept Comp & Math Sci, 1200 E Calif Blvd,MC 305-16, Pasadena, CA 91125 USA

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2021年 / 22卷 / 01期

关键词：

GAUSS MAP; GEOMETRY; VARIETIES; DIVISOR; THEOREM; CURVES; LOCUS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a solution to the weak Schottky problem for genus-five Jacobians with a vanishing theta-null, answering a question of Grushevsky and Salvati Manni. More precisely, we show that if a principally polarized Abelian variety of dimension five has a vanishing theta-null with a quadric tangent cone of rank at most three, then it is in the Jacobian locus, up to extra irreducible components. We employ a degeneration argument, together with a study of the ramification loci for the Gauss map of a theta divisor.

引用

页码：333 / 350

页数：18

共 4 条

[1] Jacobians with a vanishing theta-null in genus 4
Samuel Grushevsky
Riccardo Salvati Manni
[J]. Israel Journal of Mathematics, 2008, 164 : 303 - 315
[2] Jacobians with a vanishing theta-null in genus 4
Grushevsky, Samuel
Manni, Riccardo Salvati
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2008, 164 (01) : 303 - 315
[3] THE DIVISOR OF CURVES WITH A VANISHING THETA-NULL
BIGAS, MTI
[J]. COMPOSITIO MATHEMATICA, 1988, 66 (01) : 15 - 22
[4] Covers of degree four and the rationality of the moduli space of curves of genus five with a vanishing theta-null
Casnati, G
Del Centina, A
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 124 : 265 - 274

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