Generic flexibility of affine cones over del Pezzo surfaces in Sagemath

Abstract

Generic flexibility of affine cones over Fano varieties is a subject of active study recently. For del Pezzo surfaces the question is completely studied in degree at least 3, and partially in degree 2. We present a Sagemath module that facilitates most operations for verifying the generic flexibility of affine cones over del Pezzo surfaces and weak del Pezzo surfaces of arbitrary degree, depending on a polarization. The combinatorial approach used in this module is based on the formalism of bubble cycles and the colimit of Picard groups of blowups of the projective plane. As an example, we verify generic flexibility of affine cones over some polarizations of surfaces of degree 1 under certain conditions and over arbitrary very ample polarizations of weak del Pezzo surfaces of degree 6.