HOMOMORPHISMS OF VECTOR BUNDLES ON CURVES AND PARABOLIC VECTOR BUNDLES ON A SYMMETRIC PRODUCT

被引：0

作者：

Biswas, Indranil ^{[1
]}

Majumder, Souradeep ^{[1
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 09期

关键词：

Symmetric product; parabolic vector bundle; homomorphism; stability; MODULI;

D O I：

10.1090/S0002-9939-2012-11227-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S-n(X) be the symmetric product of an irreducible smooth complex projective curve X. Given a vector bundle E on X, there is a corresponding parabolic vector bundle V-E* on S-n(X). If E is nontrivial, it is known that V-E* is stable if and only if E is stable. We prove that H-0 (S-n (X), Hom(par)(V-E*, V-F*)) = H-0(X, F circle plus E-v)circle plus(H-0(X, F)circle plus H-0 (X, E-v)). As a consequence, the map from a moduli space of vector bundles on X to the corresponding moduli space of parabolic vector bundles on S-n(X) is injective.

引用

页码：3017 / 3024

页数：8