Éclatements quasi homogènes
Endomorphism algebras of complex tori.
Equidimensional actions of algebraic tori
Let be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on compatible with the conical structure. We show that such actions are cofree and the nullcones of associated with them are complete intersections.
Equivariant classification of 2-torus manifolds
We consider locally standard 2-torus manifolds, which are a generalization of small covers of Davis and Januszkiewicz and study their equivariant classification. We formulate a necessary and sufficient condition for two locally standard 2-torus manifolds over the same orbit space to be equivariantly homeomorphic. This leads us to count the equivariant homeomorphism classes of locally standard 2-torus manifolds with the same orbit space.
Equivariant sheaves on toric varieties
Equivariant vector bundles on toric varieties and some problems of linear algebra
Exponential sums on (Gm)n.
Extensions of toric varieties.
Families of -divisible groups with constant Newton polygon.
Fibres vectoriels homogenes sur les varietes abeliennes qui sont des tores analytiques (rigides).
Flag manifolds and the Landweber-Novikov algebra.
Fonctions d'Igusa p-adiques, polynômes de Bernstein, et polyèdres de Newton.
Gale duality for complete intersections
We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master...
Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables
GIT quotients of products of projective planes
Higher order duality and toric embeddings
The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the...
Hodge spaces of real toric varieties
Homology of tropical varieties
Homotopy Colimit of Quasi-join Diagrams
Indices of 1-forms and Newton polyhedra.
A formula of Matsuo Oka (1990) expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases (Propositions...