The nef cone of the moduli space of sheaves and strong Bogomolov inequalities

Izzet Coskun, Jack Huizenga

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Abstract

Let (X,H) be a polarized, smooth, complex projective surface, and let v be a Chern character on X with positive rank and sufficiently large discriminant. In this paper, we compute the Gieseker wall for v in a slice of the stability manifold of X. We construct explicit curves parameterizing nonisomorphic Gieseker stable sheaves of character v that become S-equivalent along the wall. As a corollary, we conclude that if there are no strictly semistable sheaves of character v, the Bayer–Macrì divisor associated to the wall is a boundary nef divisor on the moduli space of sheaves MH(v). We recover previous results for ℙ2 and K3 surfaces, and illustrate applications to higher Picard rank surfaces with an example on ℙ1 × ℙ1.

Original languageEnglish (US)
Pages (from-to)205-236
Number of pages32
JournalIsrael Journal of Mathematics
Volume226
Issue number1
DOIs
StatePublished - Jun 1 2018

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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