Variation of moduli spaces of coherent systems of dimension one and order one

TL;DR

This paper investigates how moduli spaces of certain coherent systems change as parameters vary, focusing on a quadric surface and computing their topological Euler characteristic under specific conditions.

Contribution

It provides explicit calculations of the Euler characteristic for moduli spaces of coherent systems on a quadric surface, advancing understanding of their topological variation.

Findings

Euler characteristic computed for specific moduli spaces

Wall-crossing behavior analyzed for these moduli spaces

Results depend on Chern class bounds and surface geometry

Abstract

We study the wall-crossing for moduli spaces of coherent systems of dimension one and order one on a smooth projective variety over the complex numbers. We compute the topological Euler characteristic of the moduli spaces in the particular case when the variety is a quadric surface, the first Chern class of the coherent systems is of the form (2,r) and the second Chern class is bounded from below by 3r + 1 and also by 4r - 8.