Geometry of syzygies of sheaves on ℙ² via interpolation and Bridgeland stability

2024/06/29 by Leal, Manuel, Huerta, Cesar Lozano, Ryan, Tim
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.00526

Abstract

We show that the minimal free resolution of a general semi-stable sheaf U on ℙ² contains a subcomplex that determines an extremal ray of the cone of effective divisors of its moduli space. We provide evidence that this is part of a general phenomenon in which minimal free resolutions, for distinct Betti tables, contain subcomplexes depending on wall-crossing. From this viewpoint, we provide new computations of the movable cones and Mori decompositions of some moduli spaces of sheaves using syzygies.

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