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Geometry of syzygies of sheaves on $\mathbb{P}^2$ via interpolation and Bridgeland stability

Geometry of syzygies of sheaves on $\mathbb{P}^2$ via interpolation and Bridgeland stability

We show that the minimal free resolution of a general semi-stable sheaf $U$ on $\mathbb{P}^2$ 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 …