Rationality of weighted hypersurfaces of special degree
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929220712660992 |
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| author | Chitayat, Michael |
| author_facet | Chitayat, Michael |
| contents | Let $X \subset \mathbb{P}(w_0, w_1, w_2, w_3)$ be a quasismooth well-formed weighted projective hypersurface and let $L = lcm(w_0,w_1,w_2,w_3)$. We characterize when $X$ is rational under the assumption that $L$ divides $deg(X)$ by combining an algebraic proof of rationality valid in all dimensions with a new result on numerical semigroups. As applications, we give new examples of families of normal projective rational varieties with quotient singularities and ample canonical divisor; we also determine precisely which affine Pham-Brieskorn threefolds are rational. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05324 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rationality of weighted hypersurfaces of special degree Chitayat, Michael Algebraic Geometry Commutative Algebra 14M20, 14J26, 13A02 Let $X \subset \mathbb{P}(w_0, w_1, w_2, w_3)$ be a quasismooth well-formed weighted projective hypersurface and let $L = lcm(w_0,w_1,w_2,w_3)$. We characterize when $X$ is rational under the assumption that $L$ divides $deg(X)$ by combining an algebraic proof of rationality valid in all dimensions with a new result on numerical semigroups. As applications, we give new examples of families of normal projective rational varieties with quotient singularities and ample canonical divisor; we also determine precisely which affine Pham-Brieskorn threefolds are rational. |
| title | Rationality of weighted hypersurfaces of special degree |
| topic | Algebraic Geometry Commutative Algebra 14M20, 14J26, 13A02 |
| url | https://arxiv.org/abs/2308.05324 |