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

2015/12/08 by İzzet Coşkun, Jack Huizenga, Coskun, Izzet +1
Mathematics · #14C05 #14E30 #14J29 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1512.02661

openalex publication_date 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,H) be a polarized, smooth, complex projective surface, and let v be a\nChern character on X with positive rank and sufficiently large discriminant. In\nthis paper, we compute the Gieseker wall for v in a slice of the stability\nmanifold of X. We construct explicit curves parameterizing non-isomorphic\nGieseker stable sheaves that become S-equivalent along the wall. As a\ncorollary, we conclude that if there are no strictly semistable sheaves of\ncharacter v, the Bayer-Macri divisor associated to the wall is a boundary nef\ndivisor on the moduli space of sheaves M_H(v). We recover previous results for\nthe projective plane and K3 surfaces, and illustrate applications to higher\nPicard rank surfaces with an example on a quadric surface.\n

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