Graph theoretic techniques in algebraic geometry II: construction of singular complex surfaces of the rational cohomology type of CP2.
Hodge numbers of a double octic with non-isolated singularities
If B is a surface in ℙ³ of degree 8 which is the union of two smooth surfaces intersecting transversally then the double covering of ℙ³ branched along B has a non-singular model which is a Calabi-Yau manifold. The aim of this note is to compute the Hodge numbers of this manifold.
Homogeneous polynomials with isomorphic Milnor algebras
We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.
Homology of singular cubic surfaces in .
Horikawa Surfaces with Maximal Picard Numbers.
Hypersurface sections and obstructions (rational surface singularities)
Infinitesimal Deformations of Cusp Singularities.
Inoue-Hirzebruch Surfaces and a Duality of Hyperbolic Unimodular Singularities. I.
Instanton moduli as a novel map from tori to K3-surfaces.
Integral quadratic forms : applications to algebraic geometry
Invariance of Pluri-Genera of a Degenerating Family of Algebraic Surfaces.
Jacobian discrepancies and rational singularities
Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth varieties. The resulting invariant, which we call , is closely related to the jet schemes and the Nash blow-up of the variety. This notion leads to a framework in which adjunction and inversion of adjunction hold in full generality, and several consequences are drawn from these properties. The main result of the paper...
Kodaira singularities and an extension of Arnold's strange duality
L2-cohomology and intersection homology of certain algebraic varieties with isolated singularities.
Les singularités simples elliptiques, leurs déformations, les surfaces de del Pezzo et les transformations quadratiques
Lieu discriminant d’un germe analytique de corang 1 de vers
On considère des germes d’applications analytiques de vers , de corang 1, finis, à lieu critique irréductible. De corang 1 signifie qu’il s’écrit après un bon choix de coordonnées locales sous la forme: où . On donne des conditions nécessaires et suffisantes pour qu’une courbe plane irréductible soit le lieu discriminant d’un tel germe d’applications : ce sont des conditions numériques portant sur les exposants de Puiseux. Ce problème est lié à celui de la représentation d’une variété lagrangienne...
Lieu singulier d'une surface réglée
Limit trees and generic discriminants of minimal surface singularities
According to R. Bondil the dual graph of the minimal resolution of a minimal normal surface singularity determines the generic discriminant of that singularity. In this article we give with combinatorial arguments the link between the limit trees and the generic discriminants of minimal normal surface singularities. The weighted limit trees of a minimal surface singularity determine the generic discriminant of that singularity.
Links of surface singularities and CR space forms.
Local embeddings of lines in singular hypersurfaces
Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.