On the moduli space of simple sheaves on singular K3 surfaces

Barbara Fantechi; Rosa M. Miró-Roig

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arXiv · 2403.00735

On the moduli space of simple sheaves on singular K3 surfaces

Barbara Fantechi·Rosa M. Miró-Roig

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Abstract

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof.

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Barbara Fantechi, Rosa M. Miró-Roig. 2024-03-01. On the moduli space of simple sheaves on singular K3 surfaces. https://arxiv.org/abs/2403.00735

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