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Affine cones over cubic surfaces are flexible in codimension one

Alexander Perepechko

Abstract

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

Affine cones over cubic surfaces are flexible in codimension one

Abstract

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

Paper Structure

This paper contains 7 sections, 13 theorems, 21 equations.

Table of Contents

  1. Introduction
  2. Flexibility criterion for affine cones
  3. Cubic surfaces
  4. Cones
  5. Cylinders
  6. Collections
  7. Flexibility

Key Result

Theorem \oldthetheorem

Let $X$ be an affine algebraic variety of dimension $\ge2$. Then the following conditions are equivalent:

Theorems & Definitions (32)

  • Theorem \oldthetheorem: AFKKZ
  • Definition \oldthetheorem: KPZ11
  • Lemma \oldthetheorem
  • proof
  • Definition \oldthetheorem
  • Theorem \oldthetheorem
  • proof
  • Remark \oldthetheorem
  • Definition \oldthetheorem
  • Proposition \oldthetheorem
  • ...and 22 more