An approach of the minimal model program for horospherical varieties via moment polytopes

Pasquier, Boris

doi:10.1515/crelle-2013-0103

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…An irreducible normal G-variety X is called spherical if a Borel subgroup B ⊆ G has an open orbit in X. Spherical varieties are generalizations of toric varieties. Following the equivariant Mori program for toric varieties in [Rei83], the equivariant Mori program for spherical varieties was considered by Brion and Knop in [Bri93,BK94] (see also the recent papers of Perrin and Pasquier [Per14,Pas15a]). It is known that a Q-Gorenstein spherical variety is always log-terminal (see [AB04] and [Pas15b, Proposition 5.6]).…”

Section: Victor Batyrev and Giuliano Gagliardimentioning

confidence: 99%

On the algebraic stringy Euler number

Batyrev¹,

Gagliardi

2017

Proc. Amer. Math. Soc.

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We are interested in stringy invariants of singular projective algebraic varieties satisfying a strict monotonicity with respect to elementary birational modifications in the Mori program. We conjecture that the algebraic stringy Euler number is one of such invariants. In the present paper, we prove this conjecture for varieties having an action of a connected algebraic group G and admitting equivariant desingularizations with only finitely many G-orbits. In particular, we prove our conjecture for arbitrary projective spherical varieties.

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Section: Victor Batyrev and Giuliano Gagliardimentioning

confidence: 99%

On the algebraic stringy Euler number

Batyrev¹,

Gagliardi

2017

Proc. Amer. Math. Soc.

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“…A presentation of the theory of horospherical varieties, and their relation to Fano varieties, can be found in [Pas06,Pas08]. They form a fertile ground to tackle many problems in algebraic geometry: the Mukai conjecture [Pas10], the (log) minimal model program [Pas15a,Pas18], the stringy invariants [BM13,LPR], the quantum cohomology [GPPS]... However, as far as we know, the theory of equivariant real structures on horospherical varieties has never been systematically studied.…”

Section: Introductionmentioning

confidence: 99%

Real Structures on Horospherical Varieties

Moser-Jauslin¹,

Terpereau²

2022

Michigan Math. J.

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We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of such real structures and determine the number of equivalence classes. We then apply our results to classify the equivariant real structures on smooth projective horospherical varieties of Picard rank 1. Contents Introduction 1 1. Real group structures on complex algebraic groups 5 2. Equivariant real structures on quasi-homogeneous spaces 13 3. Equivariant real structures on horospherical varieties 16 Appendix A. Tits classes for the simply-connected simple algebraic groups (by Mikhail Borovoi) 26 References 29

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“…Many difficult problems of algebraic geometry were solved for horospherical varieties (among other varieties) such as the Mukai conjecture [Pas10], the (log) minimal model program [Pas15a,Pas18a], the stringy invariants [BM13,LPR], the quantum cohomology [GPPS], or the cohomology of line bundles [CD]. However, as far as we know, the theory of equivariant real structures on horospherical varieties has never been systematically studied.…”

Section: Introductionmentioning

confidence: 99%

Real structures on horospherical varieties

Moser-Jauslin,

Terpereau,

Borovoi

2018

Preprint

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We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. We obtain a necessary and sufficient condition for the existence of an equivariant real structure on a given horospherical variety, and we determine the number of equivalence classes of equivariant real structures on horospherical homogeneous spaces. We then apply our results to classify the equivalence classes of equivariant real structures on smooth projective horospherical varieties of Picard rank 1.

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An approach of the minimal model program for horospherical varieties via moment polytopes

Cited by 7 publications

References 5 publications

On the algebraic stringy Euler number

On the algebraic stringy Euler number

Real Structures on Horospherical Varieties

Real structures on horospherical varieties

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