Geometry of moduli stacks of (k, l)-stable vector bundles over algebraic curves

JOURNAL OF GEOMETRY AND PHYSICS

卷:111

Article

Mata-Gutierrez, O.¹  Neumann, Frank² 

[1] Univ Guadalajara, CUCEI, Dept Matemat, Av Revoluc 1500, Guadalajara 44430, Jalisco, Mexico

[2] Univ Leicester, Dept Math, Univ Rd, Leicester LE1 7RH, Leics, England

关键词: Algebraic stacks;    Moduli of vector bundles;    (k,l)-stability;   

DOI  :  10.1016/j.geomphys.2016.10.003

来源: Elsevier

【 摘 要 】

We study the geometry of the moduli stack of vector bundles of fixed rank and degree over an algebraic curve by introducing a filtration made of open substacks build from (k, l)-stable vector bundles. The concept of (k, l)-stability was introduced by Narasimhan and Ramanan to study the geometry of the coarse moduli space of stable bundles. We will exhibit the stacky picture and analyse the geometric and cohomological properties of the moduli stacks of (k,l)-stable vector bundles. For particular pairs (k, l) of integers we also show that these moduli stacks admit coarse moduli spaces and we discuss their interplay. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free