Deformations and extensions of Gorenstein weighted projective spaces

Thomas Dedieu; Edoardo Sernesi

doi:10.1007/978-3-031-11938-5_5

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arXiv · 2103.08210

Deformations and extensions of Gorenstein weighted projective spaces

Thomas Dedieu·Edoardo Sernesi

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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.

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Thomas Dedieu, Edoardo Sernesi. 2021-03-15. Deformations and extensions of Gorenstein weighted projective spaces. https://doi.org/10.1007/978-3-031-11938-5_5

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