Moduli of Brill-Noether pairs on algebraic curves

TL;DR

This paper constructs coarse moduli spaces for Brill-Noether pairs, which are pairs of torsion-free sheaves and subspaces of sections on algebraic curves, applicable to singular curves and all stability parameters.

Contribution

It provides a general construction of moduli spaces for Brill-Noether pairs on arbitrary singular algebraic curves for all stability parameters.

Findings

Constructed coarse moduli spaces for Brill-Noether pairs.

Applicable to arbitrary singular curves of pure dimension.

Works for all positive rational stability parameters.

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 $\Lambda$ 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 $\alpha$ occurring in the stability condition. (Hard copies available on request.)