Cohomology bounds and Chern class inequalities for stable sheaves on a smooth projective variety

Tohru Nakashima ()
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Tohru Nakashima: Japan Women’s University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 789-796

Abstract: Abstract We give effective upper bounds for dimensions of the $$(n-1)$$ ( n - 1 ) -th cohomology groups of $$\mu $$ μ -semistable torsion-free sheaves on a smooth projective variety of dimension n defined over an algebraically closed fieled of characteristic zero. As a corollary to this result, we obtain bounds for the dimension of the moduli space of $$\mu $$ μ -stable vector bundles. We also prove Bogomolov-Gieseker type inequalities for the fourth Chern classes $$c_4(E)$$ c 4 ( E ) of $$\mu $$ μ -semistable vector bundles E on a smooth projective fourfold.

Keywords: Bogomolov-Gieseker type inequality; $$\mu $$ μ -semistable sheaves; Moduli spaces; 14J60; 14F05; 14J32 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00297-8

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