Ga-actions on affine cones

Abstract

We give a criterion of existence of a unipotent group action on the affine cone over a projective variety or, more generally, on the affine quasicone over a variety which is projective over another affine variety.

16p. In a formula in the proof of Lemma 2.3, the direct sum was replaced by the usual sum . The authors are grateful to Kevin Langlois for mentioning this inaccuracy

References in corpus (2)

• Locally nilpotent derivations on affine surfaces with a $\C^*$-action
• Affine cones over Fano threefolds and additive group actions

Cited by in corpus (13)

• Infinite transitivity on universal torsors
• The automorphism group of a rigid affine variety
• Cylinders in del Pezzo surfaces
• Cylinders in singular del Pezzo surfaces
• Affine cones over cubic surfaces are flexible in codimension one
• Infinite transitivity on affine varieties
• Super-rigid Affine Fano Varieties
• Affine cones over smooth cubic surfaces
• Cylinders in weak del Pezzo fibrations
• When is the automorphism group of an affine variety nested?
• Compactifications of the affine plane over non-closed fields
• Cylinders in canonical del Pezzo fibrations
• Unipotent Group Actions on Del Pezzo Cones