Algebraic density property of Danilov-Gizatullin surfaces

Details Algebraic density property of Danilov-Gizatullin surfaces Algebraic density property of Danilov-Gizatullin surfaces

2010-09-21

arxiv.org/abs/1009.4209v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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.

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