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arXiv · 1512.02661

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 non-isomorphic Gieseker stable sheaves 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-Macri divisor associated to the wall is a boundary nef divisor on the moduli space of sheaves M_H(v). We recover previous results for the projective plane and K3 surfaces, and illustrate applications to higher Picard rank surfaces with an example on a quadric surface.

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Izzet Coskun, Jack Huizenga. 2016-03-09. The nef cone of the moduli space of sheaves and strong Bogomolov inequalities. https://arxiv.org/abs/1512.02661

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