Deformations and extensions of Gorenstein weighted projective spaces

Abstract

We study the existence of deformations of all 14 Gorenstein weighted projective spaces P of dimension 3 by computing the number of times their general anticanonical divisors are extendable. In favorable cases (8 out of 14), we find that P deforms to a 3-dimensional extension of a general non-primitive polarized K3 surface. On our way we show that each such P in its anticanonical model satisfies property N2, and we compute the deformation space of the cone over P. This gives as a byproduct the exact number of times P is extendable.