Geometry of moduli stacks of -stable vector bundles over algebraic curves

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• 作者：O. Mata-Gutié ; rrez^a ; ^{osbaldo.mata@academico.udg.mx} ; ^{osbaldo@cimat.mx} ; Frank Neumann^b ; ^fn8@le.ac.uk
• 关键词：primary ; 14H60 ; 14D23 ; secondary ; 14D20
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：Complete
• 页码：54-70
• 全文大小：573 K
• 卷排序：111

文摘

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)(k,l)-stable vector bundles. The concept of (k,l)(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)(k,l)-stable vector bundles. For particular pairs (k,l)(k,l) of integers we also show that these moduli stacks admit coarse moduli spaces and we discuss their interplay.