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Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Fabian Reede

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 Schröer. In this paper we construct slope stable sheaves on $S_{[n]}$ and study some of their properties.

Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Abstract

Let be a K3 surface which doubly covers an Enriques surface . If is an odd number, then the Hilbert scheme of -points admits a natural quotient . This quotient is an Enriques manifold in the sense of Oguiso and Schröer. In this paper we construct slope stable sheaves on and study some of their properties.
Paper Structure (5 sections, 16 theorems, 67 equations)

This paper contains 5 sections, 16 theorems, 67 equations.

Table of Contents

  1. Stability of tautological sheaves on Hilbert schemes of points
  2. Descent of tautological sheaves to Enriques manifolds
  3. Computation of certain extension spaces
  4. Stable sheaves on Enriques manifolds
  5. Acknowledgement

Key Result

Lemma 1.2

Assume $E$ is torsion free and slope stable with respect to $h\in \mathop{\mathrm{Amp}}\nolimits(X)$ such that its double dual satisfies $E^{**}\neq \mathop{\mathrm{\mathcal{O}}}\nolimits_X$, then the associated tautological sheaf $E^{[n]}$ is slope stable with respect to some $H\in \mathop{\mathrm{

Theorems & Definitions (41)

  • Remark 1.1
  • Lemma 1.2
  • proof
  • Proposition 1.3
  • proof
  • Remark 1.4
  • Theorem 1.5
  • proof
  • Proposition 2.1
  • Remark 2.2
  • ...and 31 more