Commutative unipotent group actions on flag varieties and nilpotent multiplications

Devyatov, Rostislav

doi:10.1070/rm2014v069n05abeh004923

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Cited by 9 publications

(11 citation statements)

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“…There is a number of results on additive actions on flag varieties [1,[13][14][15], singular del Pezzo surfaces [12], Hirzebruch surfaces [17] and weighted projective planes [2].…”

Section: Introductionmentioning

confidence: 99%

Additive actions on complete toric surfaces

Dzhunusov¹

2019

Preprint

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“…There is a number of results on additive actions on flag varieties [1,[13][14][15], singular del Pezzo surfaces [12], Hirzebruch surfaces [17] and weighted projective planes [2].…”

Section: Introductionmentioning

confidence: 99%

Additive actions on complete toric surfaces

Dzhunusov¹

2019

Preprint

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“…These correspondences inspired recent works studying additive actions on projective varieties, see, e.g. [1,3,6,7,8,11].…”

Section: Introductionmentioning

confidence: 66%

Commutative actions on smooth projective quadrics

Borovik¹,

Sergey²,

Trushin³

2020

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By a commutative action on a smooth quadric Qn in P n+1 we mean an effective action of a commutative connected algebraic group on Qn with an open orbit. We show that for n ≥ 3 all commutative actions on Qn are additive actions described by Sharoiko in 2009. So there is a unique commutative action on Qn up to equivalence. For n = 2 there are three commutative actions on Q 2 up to equivalence, for n = 1 there are two commutative actions on Q 1 up to equivalence.

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“…Then we discuss a deep uniqueness result which claims that if a flag variety is not isomorphic to the projective space then it admits at most one additive action. This theorem is proved by Fu-Hwang [41] and independently by Devyatov [33]. The last part presents a construction due to Feigin [37] that degenerates arbitrary flag variety to a variety with an additive action.…”

Section: Introductionmentioning

confidence: 92%