Geodesic
Smooth Nonprojective Equivariant Completions of Affine Space
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 929-937

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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. 
@article{MZM_2021_109_6_a11,
     author = {K. V. Shakhmatov},
     title = {Smooth {Nonprojective} {Equivariant} {Completions} of {Affine} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {929--937},
     publisher = {mathdoc},
     volume = {109},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a11/}
}
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K. V. Shakhmatov. Smooth Nonprojective Equivariant Completions of Affine Space. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 929-937. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a11/