Deformations and extensions of Gorenstein weighted projective spaces

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-primitively polarized K3 surface. On our way we show that each such P in its anticanonical model satisfies property N2, i.e., its homogeneous ideal is generated by quadrics and the frist syzygies are generated by linear syzygies, and we compute the deformation space of the cone over P. This gives as a byproduct the exact number of times P is extendable.

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