Minimal resolution of general stable vector bundles on $\PP^2$

TL;DR

This paper investigates the minimal free resolutions of general stable vector bundles on the projective plane and provides a straightforward proof of the irreducibility of their moduli spaces.

Contribution

It introduces a method to determine minimal resolutions for stable bundles on 2 and offers a simple proof of the moduli space's irreducibility.

Findings

Minimal free resolutions of general stable bundles are characterized.

A simple proof of the irreducibility of the moduli space is provided.

Insights into the structure of moduli spaces of vector bundles on 2.

Abstract

We study the general elements of the moduli spaces (\MM_{\PP^2} (r, c_1, c_2) ) of stable holomorphic vector bundle on $\PP^2$ and their minimal free resolution. Incidentally, a quite easy proof of the irreducibility of (\MM_{\PP^2} (r, c_1, c_2)) is shown.