Automorphism groups on normal singular cubic surfaces with no parameters

Sakamaki, Yoshiyuki

doi:10.1090/s0002-9947-09-05023-5

Cited by 17 publications

(11 citation statements)

References 10 publications

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“…Thus, Theorem 2.1 yields that Aut(X) is the semidirect product of K * and G a . This is in accordance with [23]; we would like to thank Antonio Laface for mentioning this reference to us.…”

Section: Demazure Rootssupporting

confidence: 88%

The Automorphism Group of a Variety with Torus Action of Complexity One

Arzhantsev

Hausen²,

Herppich³

et al. 2014

MMJ

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We consider a normal complete rational variety with a torus action of complexity one. In the main results, we determine the roots of the automorphism group and give an explicit description of the root system of its semisimple part. The results are applied to the study of almost homogeneous varieties. For example, we describe all almost homogeneous (possibly singular) del Pezzo K * -surfaces of Picard number one and all almost homogeneous (possibly singular) Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus.

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“…Thus, Theorem 2.1 yields that Aut(X) is the semidirect product of K * and G a . This is in accordance with [23]; we would like to thank Antonio Laface for mentioning this reference to us.…”

Section: Demazure Rootssupporting

confidence: 88%

The Automorphism Group of a Variety with Torus Action of Complexity One

Arzhantsev

Hausen²,

Herppich³

et al. 2014

MMJ

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“…Let S be a smooth cubic surface in P 3 . Then any automorphism of the affine variety P 3 n S is induced by an automorphism of P 3 , i.e., we have Aut P 3 n S D Aut P 3 ; S : that admits an effective G a -action (see [41,147,197]). Then Aut.P 3 ; S / contains a subgroup isomorphic to G a , so that Aut.P 3 n S / also contains a subgroup isomorphic to G a .…”

Section: Cylinders In Complements To Hypersurfacesmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

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“…We denote the symmetric group on n letters by Σ n . The automorphism groups are from [25] and the GIT semi-stability assertions are from [18].…”

Section: Addressing the Orbit Closure Problemmentioning

confidence: 99%