On improper isolated intersection in complex analytic geometry
On local invariants of totally real surfaces.
On meromorphic functions defined by a differential system of order
Given a germ of holomorphic function on , we study the condition: “the ideal is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with .
On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities.
On polar invariants of hypersurface singularities
On the Bifurcation Variety of Some Non-Isolated Singularities.
On the conflict variety of an isolated hypersurface singularity.
On the monodromy at infinity of a polynomial map
On the monodromy of curve singularities.
On the versal discriminant of singularities
It is well known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ( in Arnold’s classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their work and...
Pole order filtration on the cohomology of algebraic links
Puiseux Expansion of a Cuspidal Singularity
We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.
Quantum Singularity Theory for and -Spin Theory
We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity of type our construction of the stack of -curves is canonically isomorphic to the stack of -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine proof of the...
Rank two Ulrich modules over the affine cone of the simple node.
Rationale Singularitäten komplexer Flächen.
Representation theory for log-canonical surface singularities
We consider the representation theory for a class of log-canonical surface singularities in the sense of reflexive (or equivalently maximal Cohen-Macaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumeration of the indecomposable reflexive modules is given, and we prove that any reflexive module admits an integrable connection and hence is induced from a finite dimensional representation of the local fundamental...
Seiberg-Witten invariants and surface singularities.
Semi-simple Carrousels and the Monodromy
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
Simple Singularities in Positive Characteristic.
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...