Related papers: On the geometry of spherical varieties

A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.

We discuss various phenomena of tangency in projective and convex geometry.

Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…

This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

Let $G$ be a connected reductive algebraic group. We develop a Gr\"obner theory for multiplicity-free $G$-algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space $G/H$. We define the notion of a spherical…

A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates…

Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under K\"{a}hler deformations…

We survey several results known on sampling in computational geometry.

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…

This is a survey written for a special edition of the journal of differential geometry.

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.

In this revised version, we add some expository material and references and make some minor corrections.

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…

This a collection of about 100 exercises. It could be used as a supplement to the book Koll\'ar--Mori: Birational geometry of algebraic varieties.

This is a survey article on the relationship between algebraic properties of diffeomorphism groups and homotopical properties of foliations, written for the Notices of the AMS.

This is a survey paper on the space of symplectic structures on closed 4-manifolds, for the Proceedings ICCM 2004

New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…