Related papers: Classification of two-orbit varieties

Given an action of an algebraic torus on a normal affine variety, we describe all open subsets admitting a complete orbit space.

Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…

The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such…

We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can…

We give a new proof of the classification of ${\rm GL}^+(2,\mathbb{R})$-orbit closures that are saturated for the absolute period foliation of the Hodge bundle. As a consequence, we obtain a short proof of the classification of closures of…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

We classify the convex polytopes whose symmetry groups have two orbits on the flags. These exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the…

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable…

The main result of this paper is a new parameterization of the orbits of a symmetric subgroup on a partial flag variety. The parameterization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the…

It is a classical result that the set $K\backslash G /B$ is finite, where $G$ is a reductive algebraic group over an algebraically closed field with characteristic not equal to two, $B$ is a Borel subgroup of $G$, and $K = G^{\theta}$ is…

We classify the finite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a theorem of C. L. Siegel, affine algebraic…

Moraga and Yeong conjectured that for a smooth complex projective variety $X$ of dimension $n$, an ample line bundle $A$ on $X$ and an integer $m \ge 3 n + 1$, very general elements of the adjoint linear system $|\omega_{X} \otimes…

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…

We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit…

Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…

In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two algebras in the same…

In this note I give a formula for calculating the number of orbits of irreducible binary forms of degree $n$ over GF$(p)$ under the action of GL$(2,p)$. This formula has applications to the classification of class two groups of exponent $p$…

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…

Our main result is a combinatorial characterization of when a horospherical variety has (at worst) quotient singularities. Using this characterization, we show that every quasiprojective horospherical variety with quotient singularities is…

We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to the integral Hodge conjecture for curve classes on abelian…