A comparison of deformations and geometric study of varieties of associative algebras.
A general embedding theorem in formal geometry
A note on ...-constant families of plane curves.
A period mapping for certain semi-universal deformations
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 support theorem for Hilbert schemes of planar curves
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve...
A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.
Algebraic Surfaces of General Type with Small c... . III.
Algebraic Surfaces of General Type With Small ... . IV.
Automorphismes et deformations des varietes de Borel
Automorphisms of rational double points and moduli spaces of surfaces of general type
Babylonian Tower Theorems on the Punctured Spectrum.
Calcul du nombre de cusps dans la déformation semi-universelle d'une singularité isolée d'hypersurface complexe
Codimension-two Subvarieties of IPn with the Cohomology of a Complete Intersection.
Cohen-Macaulay module type
Cohomologically insignificant degenerations of algebraic varieties
Conjecture de Bloch et nombres de Milnor
Nous déduisons de la formule du conducteur, conjecturée par S. Bloch, celle de P. Deligne exprimant, dans le cas d'une singularité isolée, la dimension totale des cycles évanescents en fonction du nombre de Milnor. En particulier, la formule de Deligne est établie en dimension relative un; en appendice, on généralise cet énoncé au cas d'un lieu singulier propre.
Correction to the paper "Moduli spaces of covers and the Hurwitz monodromy group".
Courbes de semi-groupe donné.
Curves on surfaces with multiple line.