Algebraic density property of Danilov-Gizatullin surfaces

Abstract

A Danilov-Gizatullin surface is an affine surface $V$ which is the complement of an ample section $S$ of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of $V$ depends only on the self-intersection number $S^2$. In this paper we apply their theorem to present $V$ as the quotient of an affine threefold by a torus action, and to prove that the Lie algebra generated by the complete algebraic vector fields on $V$ coincides with the set of all algebraic vector fields.

12 pages

References in corpus (1)

• Criteria for the density property of complex manifolds

Cited by in corpus (1)

• Makar-Limanov invariant, Derksen invariant, flexible points