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arXiv · 2508.13395

Moduli of non-pure sheaves and contractions of Hilbert schemes

Andres Fernandez Herrero·Svetlana Makarova
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Abstract

We define certain stacks of rank one sheaves on a smooth projective variety, and show that they admit proper good moduli spaces. We offer several applications to contractions of subschemes inside Hilbert schemes of points. We construct a surgery diagram via non-GIT wall-crossing, and use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata's DK-hypothesis in this setting.

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Andres Fernandez Herrero, Svetlana Makarova. 2025-08-18. Moduli of non-pure sheaves and contractions of Hilbert schemes. https://arxiv.org/abs/2508.13395

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