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Mathematics > Algebraic Geometry

arXiv:1812.10723 (math)
[Submitted on 27 Dec 2018]

Title:Biregular and birational geometry of quartic double solids with 15 nodes

Authors:Artem Avilov
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Abstract:Three-dimensional del Pezzo varieties of degree 2 are double covers of projective space $\mathbb{P}^{3}$ branced in a quadric. In this paper we prove that if a del Pezzo variety of degree 2 has exactly 15 nodes then the corresponding quadric is a hyperplane section of the Igusa quartic or, equivalently, all such del Pezzo varieties are members of one particular linear system on the Coble fourfold. Their automorphism groups are induced from the automorphism group of Coble fourfold. Also we classify all $G$-birationally rigid varieties of such type.
Comments: Ta appear in Izv. RAN
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1812.10723 [math.AG]
  (or arXiv:1812.10723v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.10723
Related DOI: https://doi.org/10.1007/IM8837

Submission history

From: Artem Avilov [view email]
[v1] Thu, 27 Dec 2018 13:52:50 UTC (9 KB)
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