Related papers: On the geometry of spherical varieties

The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…

The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…

These are the notes from a survey talk given at Arbeitstagung 2001 covering the author's work with Lev Borisov and Sorin Popescu on toric varieties, modular forms, and equations of modular curves.

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

We survey some results on toric topology.

We survey new results on finite groups of birational transformations of algebraic varieties.

In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…

This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

This is a topical review on the generalization of the Jordan-Wigner transformations to any spin and spatial dimensions.

We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard…

In this article we give corrections and addendum to the article ``Flops and Poisson deformations of symplectic varieties, Publ. Res. Inst. Math. Sci. {\bf 44} (2008) 259 - 314''.

We reconsider some subtle points concerning the relativistic treatment of the gravitational fields generated by spherically symmetric structures.

We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.

We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.

The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…

This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.

We give a definition of the notion of spherical varieties in the world of complex supervarieties with actions of algebraic supergroups. A characterization of affine spherical supervarieties is given which generalizes a characterization in…