The effective cone of the moduli space of sheaves on the plane

2014/01/08 by Coskun, Izzet, Huizenga, Jack, Woolf, Matthew
#13D02 #14D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary: 14J60 #Secondary: 14E30

paper · doi:10.48550/arxiv.1401.1613

Abstract

We compute the cone of effective divisors on any moduli space of semistable sheaves on the plane. The computation hinges on finding a good resolution of a general stable sheaf. This resolution is determined by Bridgeland stability and arises from a well-chosen Beilinson spectral sequence. The existence of a good choice of spectral sequence depends on remarkable number-theoretic properties of the slopes of exceptional bundles.

Related

• The geometry of the moduli space of one-dimensional sheaves
• The ample cone of moduli spaces of sheaves on the plane
• Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
• Nef and Effective Cones on the Moduli Space of Torsion Sheaves on the Projective Plane
• Geometry of syzygies of sheaves on ℙ² via interpolation and Bridgeland stability