Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles

Andres Fernandez Herrero

Published 2021-01-21Version 1

We describe an explicit Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles on a curve. It is based on the notion of parabolic slope, as in Mehta and Seshadri. We aim to give a treatment that is sheaf-theoretic and self-contained. We also prove the existence of schematic Harder-Narasimhan stratifications, which follows from an analogue of Behrend's conjecture in this context. A comparison with previous $\Theta$-stratification approaches is discussed.