Biregular and birational geometry of quartic double solids with 15 nodes
- Authors: Avilov A.A.1
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Affiliations:
- HSE University
- Issue: Vol 83, No 3 (2019)
- Pages: 5-14
- Section: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/133771
- DOI: https://doi.org/10.4213/im8837
- ID: 133771
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Abstract
Three-dimensional del Pezzo varieties of degree $2$ are double covers of$\mathbb{P}^{3}$ branched in a quartic. We prove that if a del Pezzo varietyof degree $2$ has exactly $15$ nodes, then the corresponding quartic is a hyperplanesection of the Igusa quartic or, equivalently, all such del Pezzovarieties are members of a particular linear system on the Coble fourfold.Their automorphism groups are induced from the automorphism group of theCoble fourfold. We also classify all birationally rigid varieties of thistype.
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