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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The author was supported in part by Grant-in-Aid for Scientific Research (C)(16K05111).
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Nakashima, T. Higher Brill–Noether loci and Bogomolov–Gieseker type inequality. Arch. Math. 109, 335–340 (2017). https://doi.org/10.1007/s00013-017-1067-7
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DOI: https://doi.org/10.1007/s00013-017-1067-7