Tangent cones and Lipschitz stratifications
Tangent cones at Gorenstein singularities
Technique de descente et théorèmes d'existence en géométrie algébrique. I. Généralités. Descente par morphismes fidèlement plats
The asymptotic behavior of plurigenera for a normal isolated singularity.
The Birational Geometry of Surfaces with Rational Double Points.
The branching orders of a quasi-ordinary projection.
The canonical filtration of higher dimensional purely elliptic singularity of a special type.
The category of cofinite modules for ideals of dimension one and codimension one
The cohomology of Monsky and Washnitzer
The concept of (ν)-equivalence in algebraic deformation theory
The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The Denef-Loeser series for toric surface singularities.
Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(H) in some suitable localization of the Grothendieck ring of algebraic...
The discriminant of a real simple singularity
The Discriminants of a Series of Unimodular Singularities of Space Curves.
The duality of cusp singularities.
The embedding dimension of the formal Moduli space of certain curve singularities.
The end curve theorem for normal complex surface singularities
We prove the “End Curve Theorem,” which states that a normal surface singularity with rational homology sphere link is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function whose zero set intersects in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” is described by giving an explicit set of equations describing...
The Euler characteristic of algebraic complete intersections.
The Formal Hodge Filtration.