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On the Fano dimension of an Enriques surface

Federico Tufo

Abstract

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface from six to four.

On the Fano dimension of an Enriques surface

Abstract

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface from six to four.
Paper Structure (3 sections, 7 theorems, 43 equations)

This paper contains 3 sections, 7 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. The geometric construction
  3. A general Enriques surface and its host

Key Result

Theorem 1.1

Let $S$ be a general Enriques surface. Then the Fano dimension of $S$ is $4$, i.e. there exists a Fano fourfold $Y$ with where $E_1,\ldots,\ E_9$ are exceptional bundles. The Hodge diamond of $Y$ is diagonal, and $K_0(Y)$ contains a 2-torsion class; in particular, $\mathop{\mathrm{\textnormal{D}}}\nolimits(Y)$ does not have a full exceptional collection. Such a Fano fourfold $Y$ can be realized a

Theorems & Definitions (13)

  • Theorem 1.1: \ref{['thm:main']}, \ref{['cor:main']}
  • Theorem 2.1
  • Definition 2.2
  • Lemma 2.3
  • proof
  • Proposition 2.4
  • proof
  • Remark 2.5
  • Theorem 3.1
  • proof
  • ...and 3 more