Universal families of extensions of coherent systems

TL;DR

This paper establishes cohomology and base change results for families of coherent systems on curves, proving the existence of universal extension families, which will aid in understanding wall-crossing phenomena in moduli spaces.

Contribution

It introduces the first cohomology and base change theorem for families of coherent systems and constructs universal families of extensions, extending prior work on universal extensions.

Findings

Proved cohomology and base change for coherent systems.

Constructed universal families of extensions.

Set the stage for analyzing wall-crossing in moduli spaces.

Abstract

We prove a result of cohomology and base change for families of coherent systems over a curve. We use that in order to prove the existence of (non-split, non-degenerate) universal families of extensions for families of coherent systems (in the spirit of the paper "Universal families of extensions" by H. Lange). Such results will be applied in subsequent papers in order to describe the wallcrossing for some moduli spaces of coherent systems.