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

Abstract

For every set of parabolic weights, we construct a Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles on a curve. It is based on the notion of parabolic slope, introduced by Mehta and Seshadri. We also prove that the stratification is schematic, that each stratum is complete, and establish an analogue of Behrend's conjecture for parabolic vector bundles. A comparison with recent $\Theta$-stratification approaches is discussed.

55 pages, introduction was rewritten and some sections were reorganized

References in corpus (2)

• Existence of moduli spaces for algebraic stacks
• Néron blowups and low-degree cohomological applications