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Regular version of the site

Book chapter

Group actions on affine cones

P. 123-163.
Kishimoto T., Prokhorov Y., Zaidenberg M.

In this article, the authors study the action of the additive group C on affine cones over projective varieties. They show that such actions always exist for the cones over del Pezzo surfaces of degree d≥4 which are canonically embedded, and give relations between the actions and existence of polar cylinders. The case of del Pezzo surfaces of degree 3 is still open; for example, it is not known if the variety of the equation w3+x3+y3+z3=0 in C4 admits an action of the additive group C.

In book

Group actions on affine cones
Edited by: D. Daigle, R. Ganong, M. Koras. Vol. 54: Affine Algebraic Geometry: The Russell Festschrift. Providence: American Mathematical Society, 2011.