Affine cones over cubic surfaces are flexible in codimension one
arXiv:2006.16417 · doi:10.1515/forum-2020-0191
Abstract
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.
11 pages; added an example of a flexible cone