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Regular version of the site

Article

Coble fourfold, 𝔖6-invariant quartic threefolds, and Wiman–Edge sextics

Algebra & Number Theory. 2020. Vol. 14. No. 1. P. 213-274.

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 𝔖6-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 𝔖6-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 𝔖6-representations.