Abstract
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.
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