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arXiv · 2212.04467

Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Fabian Reede
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Abstract

Let $X$ be a K3 surface which doubly covers an Enriques surface $S$. If $n\in\mathbb{N}$ is an odd number, then the Hilbert scheme of $n$-points $X^{[n]}$ admits a natural quotient $S_{[n]}$. This quotient is an Enriques manifold in the sense of Oguiso and Schr\"oer. In this paper we construct slope stable sheaves on $S_{[n]}$ and study some of their properties.

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Fabian Reede. 2022-12-08. Descent of tautological sheaves from Hilbert schemes to Enriques manifolds. https://doi.org/10.1007/s10231-024-01437-z

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