Moduli spaces of SL(r)-bundles on singular irreducible curves

Abstract

For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset $\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves of rank $r$ and degree $d$ on $X$. We prove that $\Cal U_X(r,L)$ is irreducible, when a smooth curve $Y$ specializes to $X$ and a line bundle $\Cal L$ on $Y$ specializes to $L$, the specialization of moduli space of semistable rank $r$ vector bundles on $Y$ with fixed determinant $\Cal L$ has underlying set $\Cal U_X(r,L)$. For rank 2 and 3, we show that there is a Cohen-Macaulay closed subscheme in the Gieseker space which represents a suitable moduli functor and has good specialization property.

19 pages

References in corpus (3)

• Degeneration of moduli spaces and generalized theta functions
• Degeneration of SL(n)-bundles on a reducible curve
• A Gieseker type degeneration of moduli stacks of vector bundles on curves

Cited by in corpus (6)

• Existence of semistable vector bundles with fixed determinants
• Generalization of a conjecture of Mumford
• Generators of the cohomology ring, after Newstead
• On the moduli space of singular principal G-bundles over stable curves
• A canonical decomposition of generalized theta functions on the moduli stack of Gieseker vector bundles
• Vector bundles with a fixed determinant on an irreducible nodal curve