2020
DOI: 10.48550/arxiv.2007.10113
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On uniqueness of additive actions on complete toric varieties

Abstract: By an additive action on an algebraic variety X we mean a regular effective action G n a × X → X with an open orbit of the commutative unipotent group G n a . In this paper, we give a uniqueness criterion for additive action on a complete toric variety.

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Cited by 4 publications
(4 citation statements)
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“…Equivariant compactification structures on projective hypersurfaces are studied in [2], and the case of flag varieties is studied in [1] and [5]. There are also some works on toric varieties [3], [6].…”
Section: Introductionmentioning
confidence: 99%
“…Equivariant compactification structures on projective hypersurfaces are studied in [2], and the case of flag varieties is studied in [1] and [5]. There are also some works on toric varieties [3], [6].…”
Section: Introductionmentioning
confidence: 99%
“…It was proven in [12] that a complete toric variety of dimension two which admits an additive action can have either one or two non-isomorphic additive actions. There is a description of complete toric varieties with a unique additive action [13]. In [21] projective toric hypersurfaces with additive actions are classified.…”
Section: Introductionmentioning
confidence: 99%
“…Also we present two results of Dzhunusov. The first one is a classification of additive actions on complete toric surfaces [34], and the second one is a criterion of uniqueness of an additive action on a complete toric variety [35].…”
Section: Introductionmentioning
confidence: 99%