A period mapping for certain semi-universal deformations
A Pieri-Chevalley formula in the K-theory of a -bundle.
A Pieri-type formula for even orthogonal Grassmannians
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
A Poncelet theorem in space.
A priori bounds of Castelnuovo type for cohomological Hilbert functions.
A problem of Kollár and Larsen on finite linear groups and crepant resolutions
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...
A problem on coefficient fields and equations over local rings
A procedure to calcute torsion of elliptic curves over Q.
A product formula for period integrals.
A proof of Noether's formula for the arithmetic genus of an algebraic surface
A proof of the birationality of certain BHK-mirrors
We generalize and give an elementary proof of Kelly’s refinement [9] of Shoemaker’s result [11] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the Krawitz generalization [10] of the duality in Berglund-Hübsch [2].
A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
The Witten deformation is an analytic method proposed by Witten which, given a Morse function on a smooth compact manifold , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...
A proof of the valuation property and preparation theorem
The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded o-minimal theory T. The valuation property was conjectured by van den Dries, and proved for the polynomially bounded case by van den Dries-Speissegger and for the power bounded case by Tyne. Our proof uses the transfer principle for the theory (i.e. T with an extra unary symbol denoting a proper convex subring), which-together with quantifier elimination-is due to van den...
À propos de G. A. G. R.
A propos de l' espace des modules de fibrés de rang 2 sur une courbe.
À propos de la conjecture de Manin pour les courbes elliptiques modulaires
À propos de la construction de l'espace de modules des faisceaux semi-stables sur le plan projectif
À propos de la forme hermitienne canonique d'une singularité isolée d'hypersurface
À propos de l'existence de fibrés stables sur les surfaces.