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2020 Coble fourfold, $\mathfrak S_6$-invariant quartic threefolds, and Wiman–Edge sextics
Ivan Cheltsov, Alexander Kuznetsov, Konstantin Shramov
Algebra Number Theory 14(1): 213-274 (2020). DOI: 10.2140/ant.2020.14.213

Abstract

We construct two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic). We use them to show that all 𝔖 6 -invariant three-dimensional quartics are birational to conic bundles over the quintic del Pezzo surface with the discriminant curves from the Wiman–Edge pencil. As an application, we check that 𝔖 6 -invariant three-dimensional quartics are unirational, obtain new proofs of rationality of four special quartics among them and irrationality of the others, and describe their Weil divisor class groups as 𝔖 6 -representations.

Citation

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Ivan Cheltsov. Alexander Kuznetsov. Konstantin Shramov. "Coble fourfold, $\mathfrak S_6$-invariant quartic threefolds, and Wiman–Edge sextics." Algebra Number Theory 14 (1) 213 - 274, 2020. https://doi.org/10.2140/ant.2020.14.213

Information

Received: 2 February 2019; Revised: 1 July 2019; Accepted: 1 September 2019; Published: 2020
First available in Project Euclid: 7 April 2020

zbMATH: 07180786
MathSciNet: MR4076812
Digital Object Identifier: 10.2140/ant.2020.14.213

Subjects:
Primary: 14E08
Secondary: 14E05, 14J30, 14J35, 14J45

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 1 • 2020
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