On uniqueness of additive actions on complete toric varieties

Dzhunusov, Sergey

doi:10.48550/arxiv.2007.10113

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%

Euler-symmetric complete intersection in projective space

Luo¹

2022

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Euler-symmetric projective varieties, introduced by Baohua Fu and Jun-Muk Hwang in 2020, are nondegenerate projective varieties admitting many C × -actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. In this paper, we study complete intersections in projective spaces which are Euler-symmetric. It is proven that such varieties are complete intersections of hyperquadrics and the base locus of the second fundamental form at a general point is again a complete intersection.

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Section: Introductionmentioning

confidence: 99%

Euler-symmetric complete intersection in projective space

Luo¹

2022

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“…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%

Euler-symmetric projective toric varieties and additive actions

Anton¹

2021

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Let G a be the additive group of the field of complex numbers C. We say that an irreducible algebraic variety X of dimension n admits an additive action if there is a regular action of the group G n a = G a × . . . × G a (n times) on X with an open orbit. In 2017 Baohua Fu and Jun-Muk Hwang introduced a class of Euler-symmetric varieties. They gave a classification of Euler-symmetric varieties and proved that any Euler-symmetric variety admits an additive action. In this paper we show that in the case of projective toric varieites the converse is also true. More precisely, a projective toric variety admitting an additive action is an Euler-symmetric variety with respect to any linearly normal embedding into a projective space. Also we discuss some properties of Euler-symmetric projective toric varieties.

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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%