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2--elementary rational covers of the plane

Ciro Ciliberto

Abstract

In this paper I classify, up to Cremona transformations, the Galois cover of the plane with Galois group of the form $\mathbb Z_2^r$.

2--elementary rational covers of the plane

Abstract

In this paper I classify, up to Cremona transformations, the Galois cover of the plane with Galois group of the form .
Paper Structure (40 sections, 18 theorems, 77 equations)

This paper contains 40 sections, 18 theorems, 77 equations.

Table of Contents

  1. Preliminaries
  2. Generalities
  3. The Del Pezzo and the invariant conic bundle cases
  4. Classification of rational double planes
  5. Blanc's classification
  6. Preliminaries on the invariant conic bundle case
  7. Blanc's classification in the invariant conic bundle structure case
  8. Blanc's classification in Del Pezzo case
  9. $\mathbb Z_2^r$ covers of the plane
  10. Generalities
  11. Building data
  12. Building data for $2\leqslant r\leqslant 4$
  13. The building data for $r=2$
  14. The building data for $r=3$
  15. The building data for $r=4$
  16. ...and 25 more sections

Key Result

Proposition 1.1

Let $(S,G)$ be a minimal $G$--surface with $S$ smooth and rational. Then either:

Theorems & Definitions (38)

  • Proposition 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Proposition 3.1
  • Proposition 3.2
  • Example 4.1
  • Proposition 4.2
  • proof
  • ...and 28 more