Double Veronese cones with singularities
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917484855033856 |
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| author | Prokhorov, Yuri |
| author_facet | Prokhorov, Yuri |
| contents | We study double Veronese cones -- three-dimensional del Pezzo varieties of degree one -- with terminal Gorenstein singularities. We prove sharp bounds for the number of nodes, determine the structure of the automorphism group, and establish criteria for rationality and unirationality. In particular, we exhibit a $\mathbb{Q}$-factorial nodal double Veronese cone with $21$ nodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double Veronese cones with singularities Prokhorov, Yuri Algebraic Geometry 14J45, 14J30, 14E08, 14E30 We study double Veronese cones -- three-dimensional del Pezzo varieties of degree one -- with terminal Gorenstein singularities. We prove sharp bounds for the number of nodes, determine the structure of the automorphism group, and establish criteria for rationality and unirationality. In particular, we exhibit a $\mathbb{Q}$-factorial nodal double Veronese cone with $21$ nodes. |
| title | Double Veronese cones with singularities |
| topic | Algebraic Geometry 14J45, 14J30, 14E08, 14E30 |
| url | https://arxiv.org/abs/2605.11932 |