Group actions on affine cones

By Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg. 2009

50 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2042e42732aa126a484fa25c5b17997d1beb3651

Citations in the corpus

• Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5 (2011, unknown): “x0 + xi + xj > 0, 0 = i = j = 0, (5) 2x0 + x1 + · · · + x5 > 0, (6)”