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On non-projective small resolutions

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Abstract

We construct a large class of projective threefolds with one node (aka non-degenerate quadratic singularity) such that their small resolutions are not projective.

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Acknowledgements

The author is grateful to Ivan Cheltsov and Constantin Shramov for useful discussions, and to Alexander Braverman for communicating Lemma 2.5 with an idea of its proof. It is a pleasure to thank the anonymous referees for numerous helpful suggestions, which contributed much to improvement of the text.

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Authors and Affiliations

  1. National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow, Russian Federation, 101000

    Serge Lvovski

  2. Federal Scientific Centre Science Research Institute of System Analysis at Russian Academy of Science (FNP FSC SRISA RAS), 36-1 Nakhimovskiy prosp., Moscow, Russia, 117218

    Serge Lvovski

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  1. Serge Lvovski
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Correspondence to Serge Lvovski.

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Partially supported by HSE University Basic Research Program and by Simons–IUM fellowship. The work was done according to FSI SRISA RAS research project No. 0580-2021-0007 (Reg. No. 121031300051-3).

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Lvovski, S. On non-projective small resolutions. European Journal of Mathematics 8, 551–560 (2022). https://doi.org/10.1007/s40879-022-00543-7

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  • DOI: https://doi.org/10.1007/s40879-022-00543-7

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