Descent of tautological sheaves from Hilbert schemes to Enriques manifolds. (English) Zbl 07925467
Summary: Let \(X\) be a \(\mathrm{K}3\) 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 Schröer. In this paper we construct slope stable sheaves on \(S_{[n]}\) and study some of their properties.
MSC:
| 14F06 | Sheaves in algebraic geometry |
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 14J28 | \(K3\) surfaces and Enriques surfaces |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
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