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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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Orbits of the Automorphism Group of Horospherical Varieties, and Divisor Class Group
AbstractIn 2013 Bazhov proved a criterion for two points on a complete toric variety to lie in the same orbit of the neutral component of the...
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Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one
A horospherical variety is a normal G -variety such that a connected reductive algebraic group G acts with an open orbit isomorphic to a torus bundle...
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The Ring of Conditions for Horospherical Homogeneous Spaces
These are notes of a five talks lecture series during the “Graduate Summer School in Algebraic Group Actions”, at McMaster University, June...
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Recognizing the G2-horospherical Manifold of Picard Number 1 by Varieties of Minimal Rational Tangents
Pasquier and Perrin discovered that the G 2 -horospherical manifold X of Picard number 1 can be realized as a smooth specialization of the rational...
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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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Cohomology of line bundles on horospherical varieties
A horospherical variety is a normal algebraic variety where a connected reductive algebraic group acts with an open orbit isomorphic to a torus...
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Spherical Cones: Classification and a Volume Minimization Principle
Using a variational approach, we establish the equivalence between a weighted volume minimization principle and the existence of a conical Calabi–Yau...
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Curve Neighborhoods of Schubert Varieties in the Odd Symplectic Grassmannian
Let IG( k ,2 n + 1) be the odd symplectic Grassmannian. It is a quasi-homogeneous space with homogeneous-like behavior. A very limited description of...
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Cohomology Rings of Toric Bundles and the Ring of Conditions
The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding...
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Kähler–Einstein metrics on Pasquier’s two-orbits varieties
We show that there exist Kähler–Einstein metrics on two exceptional Pasquier’s two-orbits varieties. As an application, we will provide a new example...
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The Yau–Tian–Donaldson Conjecture for Cohomogeneity One Manifolds
We prove the Yau–Tian–Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a...
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Toroidal Schubert Varieties
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads...
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The Mukai Conjecture for Fano Quiver Moduli
We verify the Mukai conjecture for Fano quiver moduli spaces associated to dimension vectors in the interior of the fundamental domain.
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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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Morelli-Włodarczyk cobordism and examples of rooftop flips
We introduce the notion of rooftop flip, namely a small modification among normal projective varieties which is modeled by a smooth projective...
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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...
