38,117 research outputs found
The variety of reductions for a reductive symmetric pair
We define and study the variety of reductions for a reductive symmetric pair
(G,theta), which is the natural compactification of the set of the Cartan
subspaces of the symmetric pair. These varieties generalize the varieties of
reductions for the Severi varieties studied by Iliev and Manivel, which are
Fano varieties.
We develop a theoretical basis to the study these varieties of reductions,
and relate the geometry of these variety to some problems in representation
theory. A very useful result is the rigidity of semi-simple elements in
deformations of algebraic subalgebras of Lie algebras.
We apply this theory to the study of other varieties of reductions in a
companion paper, which yields two new Fano varieties.Comment: 23 page
Equivariant Cohomology of Rationally Smooth Group Embeddings
We describe the equivariant cohomology ring of rationally smooth projective
embeddings of reductive groups. These embeddings are the projectivizations of
reductive monoids. Our main result describes their equivariant cohomology in
terms of roots, idempotents, and underlying monoid data. Also, we characterize
those embeddings whose equivariant cohomology ring is obtained via restriction
to the associated toric variety. Such characterization is given in terms of the
closed orbits.Comment: 25 pages. Final version. To appear in Transformation Group
Holomorphic discs and sutured manifolds
In this paper we construct a Floer-homology invariant for a natural and wide
class of sutured manifolds that we call balanced. This generalizes the Heegaard
Floer hat theory of closed three-manifolds and links. Our invariant is
unchanged under product decompositions and is zero for nontaut sutured
manifolds. As an application, an invariant of Seifert surfaces is given and is
computed in a few interesting cases.Comment: This is the version published by Algebraic & Geometric Topology on 4
October 200
An Algorithm for Computing the Limit Points of the Quasi-component of a Regular Chain
For a regular chain , we propose an algorithm which computes the
(non-trivial) limit points of the quasi-component of , that is, the set
. Our procedure relies on Puiseux series expansions
and does not require to compute a system of generators of the saturated ideal
of . We focus on the case where this saturated ideal has dimension one and
we discuss extensions of this work in higher dimensions. We provide
experimental results illustrating the benefits of our algorithms
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