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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.00526 |
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Table of Contents:
- 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 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.