Semigroup of a quasiordinary singularity
Simple Singularities in Positive Characteristic.
Simultaneous Resolution of Threefold Double Points.
Singular sufaces and the rigidity of IP3.
Singularités de Klein - I
Singularités de Klein - II
Singularités imposables en position générale à une hypersurface projective
Singularities of Algebraic Surfaces with C* Action.
Singularities on complete algebraic varieties
We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.
Small Deformation of Normal Singularities (Erratum).
Small Deformations of Normal Singularities.
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Smooth double subvarieties on singular varieties, III
Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F is a (N-1)-fold...
Smoothing Cusp Singularities of Small Length.
Smoothings of cusp singularities via triangle singularities
Some geometric aspects of Puiseux surfaces.
This paper is part of the author's thesis, recently presented, where the following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series) , using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well known results for the quasi-ordinary case can be extended to this much wider family.
Some properties of double point schemes
Specialization of Segre classes of singular algebraic varieties.
Specialization to the tangent cone and Whitney equisingularity
Let be a reduced, equidimensional germ of an analytic singularity with reduced tangent cone . We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part of the specialization to the tangent cone to satisfy Whitney’s conditions along the parameter axis . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of which establishes the Whitney equisingularity of and its tangent cone under...
Spectral Pairs, Mixed Hodge Modules, and Series of Plane Curve Singularities.