2019
DOI: 10.48550/arxiv.1908.03563
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Additive actions on complete toric surfaces

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 classification of additive actions on complete toric surfaces.

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Cited by 3 publications
(6 citation statements)
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References 12 publications
(15 reference statements)
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“…Therefore, a maximal unipotent subgroup of the group Aut(X) has dimension 2, but there is no additive action on the variety X by Lemma 1. Now let us recall the main result of [15] and explain the connection between this result and Theorem 4. Definition 7.…”
Section: Corollaries and Examplesmentioning
confidence: 91%
See 2 more Smart Citations
“…Therefore, a maximal unipotent subgroup of the group Aut(X) has dimension 2, but there is no additive action on the variety X by Lemma 1. Now let us recall the main result of [15] and explain the connection between this result and Theorem 4. Definition 7.…”
Section: Corollaries and Examplesmentioning
confidence: 91%
“…In [15], all additive actions on a complete toric surface were classified. It turns out that there are no more than two non-isomorphic additive actions on a complete toric surface, see Section 7 of this work for more details.…”
Section: Introductionmentioning
confidence: 99%
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“…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%
“…There are several results on additive actions on projective hypersurfaces [4,6,17], flag varieties [1,10,13,14], singular del Pezzo surfaces [9], weighted projective planes [2] and general toric varieties [5,11,12].…”
Section: Introductionmentioning
confidence: 99%