Deformations and extensions of Gorenstein weighted projective spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916668608872448 |
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| author | Dedieu, Thomas Sernesi, Edoardo |
| author_facet | Dedieu, Thomas Sernesi, Edoardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_08210 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Deformations and extensions of Gorenstein weighted projective spaces Dedieu, Thomas Sernesi, Edoardo Algebraic Geometry 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. |
| title | Deformations and extensions of Gorenstein weighted projective spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2103.08210 |