Flexibility in affine and projective geometry
Mikhail Zaidenberg
(Institut Fourier, Grenoble)

The talk consists in two parts. In the first part, flexible affine varieties are defined, different criteria of flexibility are discussed, numerous examples and constructions of flexible varieties are presented. In the second part, we present results on flexibility of affine cones over Fano varieties of dimension 2, 3 and 4. For instance, del Pezzo cones demonstrate flexibility in degree greater than 3 and rigidity in degree less than 4. The talk is based on work of a number of persons; their names will be mentioned.