Group actions on affine cones

Details Group actions on affine cones Group actions on affine cones

2009-05-28

arxiv.org/abs/0905.4647v2

Mathematics

Algebraic Geometry

41p

Scientific paper

We address the following question: Determine the affine cones over smooth projective varieties which admit an action of a connected algebraic group different from the standard C*-action by scalar matrices and its inverse action. We show in particular that the affine cones over anticanonically embedded smooth del Pezzo surfaces of degree at least 4 possess such an action. A question by Flenner and the third author whether this is also true for cubic surfaces, occurs to be out of reach for our methods. Nevertheless, we provide a general geometric criterion that could be helpful also in this case.

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