Higher Brill-Noether loci and Bogomolov-Gieseker type inequality

摘要

We discuss the Brill-Noether loci of the moduli of mu-stable sheaves on a smooth projective variety, and obtain some necessary conditions for these loci to be non-empty. As an application of our result, we prove Bogomolov-Gieseker type inequalities concerning the third Chern character of the mu-stable sheaves on Calabi-Yau threefolds.