Families of -symplectic metrics on full flag manifolds.
Fano manifolds of degree ten and EPW sextics
O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
Finiteness of cominuscule quantum -theory
The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and whose domains...
Flag Manifolds and the Hook Formula.
Flag manifolds and the Landweber-Novikov algebra.
Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups
Générateurs explicites du groupe de Chow du schéma de Hilbert des cubiques de IP(3, C).
Geometry and cohomology of certain domains in the complex projective space.
Geometry and deformation of special Schubert varieties
Geometry of the genus 9 Fano 4-folds
We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.
Geometry on grassmannians and applications to splitting bundles and smoothing cycles
Group law on the intersection of two quadrics
Hilbert series of the Grassmannian and -Narayana numbers
We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the -Hilbert series is a Vandermonde-like determinant. We show that the -polynomial of the Grassmannian coincides with the -Narayana polynomial. A simplified formula for the -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the -Narayana numbers, i.e. the -polynomial...
Hirzebruch's Proportionality Theorem in the Non-Compact Case.
Homogene Räume k-affinoider Gruppen.
Homogeneous Algebraic Varieties Defined by Jordan Pairs.
Homologie du groupe linéaire et polylogarithmes
Homology of the Steinberg variety and Weyl group coinvariants.
How to draw tropical planes.
Hypersurfaces of the Flag Variety: Deformation theory and the Theorems of Kodaira-Spencer, Torelli, Lefschetz, M. Noether and Serre.