차수 2인 Del Pezzo곡면 위 Affine Cone의 Generic Flexibility에 관하여

Abstract

The existence of ample polar cylinders in a smooth projective variety is closely related to the existence of nontrivial additive group actions on the corresponding generalized cone, even more to the flexibility of the cone. In particular, for del Pezzo surfaces of degrees at least 3, it was completely known that their ample polar cylindricity as well as the flexibility or generic flexibility of corresponding affine cones. In addition various ample divisors on smooth del Pezzo surfaces of degree $2$ have been verified to allow polar cylinders in \cite{CPW3}. From these cylinders, we show that affine cones over smooth del Pezzo surfaces of degree $2$ polarized by such ample divisors are flexible in codimension one.