Genus 2 curves and generalized theta divisors

被引：5

作者：

Brivio, Sonia ^{[1
]}

Favale, Filippo F. ^{[1
]}

机构：

[1] Univ Milano Bicocca, Dept Math, Via Roberto Cozzi 55, I-20125 Milan, MI, Italy

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2019年 / 155卷

关键词：

Moduli spaces; Semistable vector bundles; Theta divisors; STABLE VECTOR-BUNDLES; MODULI SPACES; VARIETIES; RATIONALITY;

D O I：

10.1016/j.bulsci.2019.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate generalized theta divisors Theta(r) in the moduli spaces U-C(r,r) of semistable vector bundles on a curve C of genus 2. We provide a desingularization Phi of Theta(r) in terms of a projective bundle pi : P(V) -> U-C (r - 1, r) which parametrizes extensions of stable vector bundles on the base by O-C. Then, we study the composition of Phi with the well known theta map theta. We prove that, when it is restricted to the general fiber of pi, we obtain a linear embedding. (C) 2019 Elsevier Masson SAS. All rights reserved.

引用

页码：112 / 140

页数：29

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[2]

Atiyah Michael F., 1957, Trans. Amer. Math. Soc., V85, P181

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