Related papers: On the geometry of spherical varieties

This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…

We investigate qualitative and quantitative properties of anti-holomorphic involutions on some spherical varieties.

We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.

These are expanded notes from lectures on the geometry of spherical varieties given in Sanya. We review some aspects of the geometry of spherical varieties. We first describe the structure of $B$-orbits. Using the local structure theorems,…

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…

This paper surveys some results and methods in topological transformation groups.

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…

We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.

This is a survey article devoted to the study of real structures on complex algebraic varieties endowed with a reductive group action.

This is a survey on coarse geometry with an emphasis on coarse homology theories.

Spectral triples on the q-deformed spheres of dimension two and three are reviewed.

This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.

Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.

The possible spatial transformation properties of tetrons are discussed.

We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.

This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include…

This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…