This article is cited in 2 papers

Smooth Nonprojective Equivariant Completions of Affine Space

K. V. Shakhmatov<sup>ab

a</sup> Lomonosov Moscow State University
^b National Research University "Higher School of Economics", Moscow

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.

Keywords: nonprojective variety, toric variety, additive action, completion.

UDC: 512.745

Received: 11.03.2020

DOI: 10.4213/mzm12717

 English version: Mathematical Notes, 2021, 109:6, 954–961

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