Moduli of Brill-Noether pairs on algebraic curves

Abstract

We construct coarse moduli spaces for `Brill-Noether pairs'. Such a pair consists of a torsion-free sheaf $E$ over an algebraic curve $X$ and a vector subspace $Λ$ of its space of sections $H^0(E)$. The construction works for an arbitrary singular curve $X$ of pure dimension and for all values of the positive rational parameter $α$ occurring in the stability condition. (Hard copies available on request.)