Rational curves on homogeneous cones.
Elliptic curves on spinor varieties
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
Deux composantes du bord de
Nous étudions deux nouvelles composantes irréductibles du bord de la variété des instantons de degré 3. Nous décrivons grâce aux transformations cubo-cubiques involutives déduites de la monade de Beilinson (ce sont des transformations de Cremona particulières). Nous exhibons alors les deux composantes du bord par dégénérescence sur les transformations. Nous mettons en évidence la dualité qui les lie : les transformations cubo-cubiques de l’une sont les inverses de l’autre. Nous décrivons en...
Spherical varieties and Wahl’s conjecture
Using the theory of spherical varieties, we give a type independent very short proof of Wahl’s conjecture for cominuscule homogeneous varieties for all primes different from 2.
Courbes rationnelles sur les variétés homogènes
Soit une variété homogène sous un groupe . Nous étudions les orbites maximales de sous l’action d’un parabolique de . Nous les décomposons en fibrations affines et projectives. Cette description permet de montrer que le schéma de Hilbert des courbes rationnelles lisses de classe fixée est non vide et irréductible.
Springer fiber components in the two columns case for types and are normal
We study the singularities of the irreducible components of the Springer fiber over a nilpotent element with in a Lie algebra of type or (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.
Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics
The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, finding an efficient method to simulate the numerical solution of PB equation is very useful. As a first step, we establish in this paper a probabilistic interpretation of the nonlinear PB equation with Backward Stochastic Differential Equations...
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...
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