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On extra-special Enriques surfaces

Gebhard Martin, Giacomo Mezzedimi, Davide Cesare Veniani

Abstract

We refine Cossec and Dolgachev's classification of extra-special Enriques surfaces, providing a complete and concise proof.

On extra-special Enriques surfaces

Abstract

We refine Cossec and Dolgachev's classification of extra-special Enriques surfaces, providing a complete and concise proof.
Paper Structure (6 sections, 15 theorems, 5 equations)

This paper contains 6 sections, 15 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Genus one fibrations
  4. Isotropic sequences
  5. Non-extendable 2-sequences
  6. Special genus one fibrations with a fiber of type II*

Key Result

theorem 1

If $X$ is not extra-special of type $\tilde{E}_8$, then every $1$-sequence on $X$ extends to a $2$-sequence.

Theorems & Definitions (25)

  • definition 1
  • theorem 1: Cossec.Dolgachev or CossecDolgachevLiedtke
  • theorem 2
  • remark 1
  • remark 2
  • corollary 1
  • corollary 2
  • lemma 1: CossecDolgachevLiedtke
  • lemma 2: CossecDolgachevLiedtke
  • lemma 3: Cossec.Dolgachev or CossecDolgachevLiedtke
  • ...and 15 more