Limit points and additive group actions

Arzhantsev, Ivan

doi:10.1007/s11587-021-00630-z

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…Subsection 1. 4 Following Hassett and Tschinkel [62], in § 1.5 we establish a correspondence between (a) the faithful cyclic representations ρ : G n a → GL m (K); (b) the pairs (A, U ), where A is a local commutative associative unital algebra of dimension m with maximal ideal m, and U ⊆ m is a subspace of dimension n generating the algebra A; (c) the non-degenerate ideals I ⊆ K[S 1 , . .…”

Section: Equivariant Embeddings Into Projective Spacesmentioning

confidence: 99%

“…For example, if an affine variety X admits two actions of the torus G m that do not commute, then X admits a non-trivial G a -action (see [47], § 3, and [7], the proof of Theorem 2.1). Further, it was shown in [4], Theorem 1, that the existence of a G m -action of parabolic type on a normal affine variety implies the existence of a non-trivial G a -action. Theorem 5.5 can also be regarded as a result of this form.…”

Section: Euler-symmetric Varietiesmentioning

confidence: 99%

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Equivariant completions of affine spaces

Arzhantsev¹,

Zaitseva²

2022

Russian Math. Surveys

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We survey recent results on open embeddings of the affine space $\mathbb{C}^n$ into a complete algebraic variety $X$ such that the action of the vector group $\mathbb{G}_a^n$ on $\mathbb{C}^n$ by translations extends to an action of $\mathbb{G}_a^n$ on $X$. We begin with the Hassett-Tschinkel correspondence describing equivariant embeddings of $\mathbb{C}^n$ into projective spaces and present its generalization for embeddings into projective hypersurfaces. Further sections deal with embeddings into flag varieties and their degenerations, complete toric varieties, and Fano varieties of certain types. Bibliography: 109 titles.

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Section: Equivariant Embeddings Into Projective Spacesmentioning

confidence: 99%

Section: Euler-symmetric Varietiesmentioning

confidence: 99%

Equivariant completions of affine spaces

Arzhantsev¹,

Zaitseva²

2022

Russian Math. Surveys

Self Cite

View full text Add to dashboard Cite

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Equivariant completions of affine spaces

Arzhantsev¹,

Zaitseva²

2022

Uspekhi Mat. Nauk

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Работа содержит обзор недавних результатов об открытых вложениях аффинного пространства $\mathbb{C}^n$ в полные алгебраические многообразия $X$, для которых действие векторной группы $\mathbb{G}_a^n$ на $\mathbb{C}^n$ параллельными переносами продолжается до действия $\mathbb{G}_a^n$ на $X$. В первой части работы мы подробно изучаем соответствие Хассетта-Чинкеля, описывающее эквивариантные вложения $\mathbb{C}^n$ в проективные пространства, и приводим его обобщение на случай вложений в проективные гиперповерхности. Последующие разделы посвящены изучению вложений в многообразия флагов и в их вырождения, в полные торические многообразия и в многообразия Фано определeнных типов. Библиография: 109 названий.

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Limit points and additive group actions

Cited by 2 publications

References 18 publications

Equivariant completions of affine spaces

Equivariant completions of affine spaces

Equivariant completions of affine spaces

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