Tangencies of generic real projective hypersurfaces.
The Bifurcation Set and Logarithmic Vector Fields.
The Birational Geometry of Surfaces with Rational Double Points.
The canonical filtration of higher dimensional purely elliptic singularity of a special type.
The ?-constant stratum is not smooth.
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 Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The Local Nash problem on arc families of singularities
This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.
The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Milnor number of functions on singular hypersurfaces
The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical...
The monodromy of a series of hypersurface singularities.
The Nash problem of arcs and the rational double points
This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points ().
The plurigenera of Gorenstein surface singularities.
The real Seifert form and the spectral pairs of isolated hypersurface singularities
The second Brauer-Thrall conjecture for isolated singularities of excellent hypersurfaces.
The smooth surfaces on cubic hypersurface in P... with isolated singularities.
The Smoothing Components of a Triangle Singularity. II.
The Tangent Bundle of a Ruled Surface.