On the zero set of semi-invariants for quivers
Optimal destabilizing vectors in some Gauge theoretical moduli problems
We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...
Orbifold-Hodge numbers of Hilbert schemes
Orbites de semi-groupes de morphismes réguliers et systèmes non linéaires en temps discret.
Orbits, Invariants, and Representations Associated to Involutions of Reductive Groups.
Orbits of the Weyl group and a theorem of DeConcini and Procesi
Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants
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...
Partial flags and parabolic group actions.
Pencils of binary quartics
Perfect stratifications and theory of weights.
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.
PGL (4) acts transitively on M (-1,2).
Pinceaux de droites et automorphismes des surfaces affines.
Plane curves with small linear orbits, I
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...
Polynomial bounds for abelian groups of automorphisms
Polynomial invariants of representations of quivers.
Predegree Polynomials of Plane Configurations in Projective Space
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,...
Principal bundles admitting a rational section.
Principal bundles on affine space and bundles on the projective line.
Projective homogeneous varieties birational to quadrics.
Projective normality of flag varieties and Schubert varieties.