### References & Citations

# Mathematics > Algebraic Geometry

# Title: Deformations and extensions of Gorenstein weighted projective spaces

(Submitted on 15 Mar 2021 (v1), last revised 10 Sep 2021 (this version, v3))

Abstract: We study the existence of deformations of all $14$ Gorenstein weighted projective spaces $\mathbf P$ 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 $\mathbf P$ deforms to a $3$-dimensional extension of a general non-primitive polarized $K3$ surface. On our way we show that each such $\mathbf P$ in its anticanonical model satisfies property $N_2$, and we compute the deformation space of the cone over $\mathbf P$. This gives as a byproduct the exact number of times $\mathbf P$ is extendable.

## Submission history

From: Thomas Dedieu [view email]**[v1]**Mon, 15 Mar 2021 08:41:59 GMT (23kb)

**[v2]**Tue, 23 Mar 2021 14:22:31 GMT (23kb)

**[v3]**Fri, 10 Sep 2021 08:57:22 GMT (26kb)

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