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Families of canonical local periods on spherical varieties
We consider the variation of canonical local periods on spherical varieties proposed by Sakellaridis–Venkatesh in families. We formulate conjectures...
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Equivariant Cobordism of Smooth Projective Spherical Varieties
We study the equivariant cobordism rings for the action of a torus T on smooth varieties over an algebraically closed field of characteristic zero....
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A classification of spherical Schubert varieties in the Grassmannian
Let L be any standard Levi subgroup which acts by left multiplication on a Schubert variety X ( w ) in the Grassmannian. We give a complete...
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Applications of homogeneous fiber bundles to the Schubert varieties
This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over...
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Spherical Schubert varieties and pattern avoidance
A normal variety X is called H - spherical for the action of the complex reductive group H if it contains a dense orbit of some Borel subgroup of H . We...
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Segre Varieties
In this chapter we develop the necessary machinery for working with Segre varieties associated with real analytic hypersurfaces and give some...
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Horospherical 2-Fano varieties
We classify 2-Fano horospherical varieties with Picard number 1. We also review all the known examples of 2-Fano manifolds and investigate the...
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Spherical tropicalization and Berkovich analytification
Let X be a spherical variety. We show that Tevelev and Vogiannou’s tropicalization map from X to its tropicalization factors through the Berkovich...
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The Manin–Peyre conjecture for smooth spherical Fano threefolds
The Manin–Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N . Together with the previously solved...
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On the Existence of B -Root Subgroups on Affine Spherical Varieties
AbstractLet X be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group G . In this...
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Arithmetic fundamental lemma for the spherical Hecke algebra
We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity...
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Construction and characterisation of the varieties of the third row of the Freudenthal–Tits magic square
We characterise the varieties appearing in the third row of the Freudenthal–Tits magic square over an arbitrary field, in both the split and...
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Momentum polytopes of projective spherical varieties and related Kähler geometry
We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This...
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SPHERICAL ACTIONS ON ISOTROPIC FLAG VARIETIES AND RELATED BRANCHING RULES
Let G be a symplectic or special orthogonal group, let H be a connected reductive subgroup of G , and let X be a flag variety of G . We classify all...
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Gorensteinness and iteration of Cox rings for Fano type varieties
We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those...
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Valuative stability of polarised varieties
Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been...
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A Gallery Model for Affine Flag Varieties via Chimney Retractions
This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat–Tits buildings. We...
