On coherent systems with fixed determinant

TL;DR

This paper investigates the moduli spaces of coherent systems with fixed determinants on algebraic curves, establishing sharp bounds for their dimensions, thus advancing understanding in this specialized area of algebraic geometry.

Contribution

It demonstrates that certain lower bounds for the dimensions of fixed determinant moduli spaces, previously established by Osserman, are actually sharp, providing precise dimension estimates.

Findings

Some of Osserman's bounds are sharp.

Established exact dimension estimates for fixed determinant moduli spaces.

Extended understanding of the structure of these moduli spaces.

Abstract

Over the past 20 years, a great deal of work has been done on the moduli spaces of coherent systems on algebraic curves. Until recently, however, there has been very little work on the fixed determinant case, except for the special case of rank 2 and canonical determinant. This situation has changed due to two papers of B. Osserman, who has obtained lower bounds for the dimensions of the fixed determinant moduli spaces in some cases. Our object in this paper is to show that some of Osserman's bounds are sharp.