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Smooth Nonprojective Equivariant Completions of Affine Space

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Abstract

An open translation-equivariant embedding of the affine space \(\mathbb A^n\) into a complete nonprojective algebraic variety \(X\) is constructed for any \(n\ge 3\). The main tool is the theory of toric varieties. In the case \(n=3\), the orbit structure of the obtained action on the variety \(X\) is described.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    K. V. Shakhmatov

  2. National Research University Higher School of Economics, Moscow, 101000, Russia

    K. V. Shakhmatov

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  1. K. V. Shakhmatov
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Correspondence to K. V. Shakhmatov.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 929-937 https://doi.org/10.4213/mzm12717.

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Shakhmatov, K.V. Smooth Nonprojective Equivariant Completions of Affine Space. Math Notes 109, 954–961 (2021). https://doi.org/10.1134/S0001434621050291

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  • DOI: https://doi.org/10.1134/S0001434621050291

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