Tangent cones and Lipschitz stratifications
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 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 duality of cusp 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 fundamental group for the complement of Cayley's singularities.
The Fundamental Group of the Complement of an Algebraic Curve.
The Geometry of Representations of Am .
The homology groups of the links of quasi-ordinary singularities.
The infinitesimal M. Noether theorem for singularities
The jump of the Milnor number in the X 9 singularity class
The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.
The Le varieties, II.
The Łojasiewicz gradient inequality in a neighbourhood of the fibre
Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Milnor Number and Deformations of Complex Curve Singularities.
The monodromy of a series of hypersurface singularities.