Stability of homogeneous bundles on P^3

TL;DR

This paper investigates the stability of certain homogeneous bundles on projective 3-space using quiver representations, demonstrating stability for bundles supported on parallelepiped quivers and specific free resolutions.

Contribution

It introduces a method to determine stability of homogeneous bundles on P^3 via quiver support analysis and identifies classes of stable bundles with specific resolutions.

Findings

Bundles supported on parallelepiped quivers are stable.

Bundles with certain minimal free resolutions are proven stable.

Abstract

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver representation is a parallelepiped are stable, for instance the bundles E whose minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1 +s, l_2, l_3} V (t+s) --> E --> 0 are stable.