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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and CS, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Izzet Coskun

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Jack Huizenga

Authors
  1. Izzet Coskun
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  2. Jack Huizenga
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Correspondence to Izzet Coskun.

Additional information

During the preparation of this article the first author was partially supported by the NSF CAREER grant DMS-0950951535 and NSF grant DMS-1500031.

During the preparation of this article the second author was partially supported by a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.

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Coskun, I., Huizenga, J. The nef cone of the moduli space of sheaves and strong Bogomolov inequalities. Isr. J. Math. 226, 205–236 (2018). https://doi.org/10.1007/s11856-018-1687-z

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  • DOI: https://doi.org/10.1007/s11856-018-1687-z

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