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Non-rational sextic double solids

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Abstract

We study double solids branched along nodal sextic surfaces in a projective space and the 2-torsion subgroups in the third integer cohomology groups of their resolutions of singularities. These groups can be considered as obstructions to rationality of the double solids. Studying these groups we conclude that all sextic double solids admitting non-trivial obstructions to rationality are branched along determinantal surfaces of very specific type and we provide an explicit list of them.

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Acknowledgements

I am grateful to my advisor, Constantin Shramov, for suggesting this problem as well as for his patience and invaluable support. I also thank Anton Fonarev and Lyalya Guseva for useful discussions. I was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.

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  1. Department of Mathematics, National Research University Higher School of Economics, Russian Federation, 6 Usacheva St., 119048, Moscow, Russia

    Alexandra Kuznetsova

  2. École Polytechnique, France, CMLS, Route de Saclay, 91128, Palaiseau, France

    Alexandra Kuznetsova

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  1. Alexandra Kuznetsova
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Correspondence to Alexandra Kuznetsova.

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Kuznetsova, A. Non-rational sextic double solids. Math. Z. 301, 4015–4036 (2022). https://doi.org/10.1007/s00209-022-03040-5

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  • DOI: https://doi.org/10.1007/s00209-022-03040-5

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