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Rationality of Fano threefolds with terminal Gorenstein singularities, II

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Abstract

We classify nonrational Fano threefolds X with terminal Gorenstein singularities such that \(\mathrm {{\text {rk}}}\, \mathrm {{\text {Pic}}}(X)=1\), \((-K_X)^3\ge 8\), and \(\mathrm {{\text {rk}}}\, \mathrm {{\text {Cl}}}(X)\le 2\).

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Acknowledgements

The author would like to thank Alexander Kuznetsov for fruitful discussions and the anonymous referee for careful reading the first version of the paper and useful comments.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Yuri Prokhorov

  2. Faculty of Mathematics, Moscow State University, Moscow, Russia

    Yuri Prokhorov

  3. AG Laboratory, HSE University, Moscow, Russia

    Yuri Prokhorov

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Correspondence to Yuri Prokhorov.

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Prokhorov, Y. Rationality of Fano threefolds with terminal Gorenstein singularities, II. Rend. Circ. Mat. Palermo, II. Ser 72, 1797–1821 (2023). https://doi.org/10.1007/s12215-022-00773-4

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  • DOI: https://doi.org/10.1007/s12215-022-00773-4

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