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The set of conjugacy classes appearing in a product of conjugacy classes in a compact,
-connected Lie group can be identified with a convex polytope in the Weyl alcove.
In this paper we identify linear inequalities defining this polytope. Each inequality
corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety
, where is the complexification of and is a maximal parabolic subgroup.
This generalizes the results for of Agnihotri and the second author and Belkale
on...
In this paper we emphasize Deligne's theory of weights, in order to prove that some stratifications of algebraic varieties are perfect. In particular, we study in some detail the Bialynicki-Birula's stratifications and the stratifications considered by F. Kirwan to compute the cohomology of symplectic or geometric quotients. Finally we also appoint the motivic formulation of this approach, which contains the Hodge theoretic formulation.
The “linear orbit” of a plane curve of degree is its orbit in under the natural action of . In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for...
2000 Mathematics Subject Classification: 14N10, 14C17.We work over an algebraically closed field of characteristic zero. The group PGL(4) acts naturally on PN which parameterizes surfaces of a given degree in P3. The orbit of a surface under this action is the image of a rational map PGL(4) ⊂ P15→PN. The closure of the orbit is a natural and interesting object to study. Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above map restricted to a general Pj,...
Chevalley’s theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian variety over an arbitrary field to be a smooth connected -group in which every smooth connected affine normal -subgroup is trivial. This gives a new point of view on the classification of algebraic groups: every smooth connected group over a field is an extension...
Let be a field of characteristic . Let be a over (i.e., an -truncated Barsotti–Tate group over ). Let be a -scheme and let be a over . Let be the subscheme of which describes the locus where is locally for the fppf topology isomorphic to . If , we show that is pure in , i.e. the immersion is affine. For , we prove purity if satisfies a certain technical property depending only on its -torsion . For , we apply the developed techniques to show that all level ...
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