A functorial approach to the stability of vector bundles

Abstract

On a normal projective variety the locus of $\mu$-stable bundles that remain $\mu$-stable on all Galois covers prime to the characteristic is open in the moduli space of Gieseker semi-stable sheaves. On a smooth projective curve of genus at least 2 this locus is big in the moduli space of stable bundles, i.e., its complement has codimension at least 2.

final version to appear in mathz. improved exposition; appendix can still be found in the authors thesis. results unchanged

References in corpus (2)

• Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
• Descent theory of simple sheaves on $C_1$-fields