Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities

Milnor Number of Weighted-Lê–Yomdin Singularities

Rigid and Complete Intersection Lagrangian Singularities

In this article we prove a rigidity theorem for lagrangian singularities by studying the local cohomology of the lagrangian de Rham complex that was introduced in [SvS03]. The result can be applied to show the rigidity of all open swallowtails of dimension ≥ 2. In the case of lagrangian complete intersection singularities the lagrangian de Rham complex turns out to be perverse. We also show tha...

Milnor Numbers of Projective Hypersurfaces with Isolated Singularities

Let V be a projective hypersurface of fixed degree and dimension which has only isolated singular points. We show that, if the sum of the Milnor numbers at the singular points of V is large, then V cannot have a point of large multiplicity, unless V is a cone. As an application, we give an affirmative answer to a conjecture of Dimca and Papadima.

Complete Intersection Singularities of Splice Type as Universal Abelian Covers

It has long been known that every quasi-homogeneous normal complex surface singularity with Q–homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called “splice type singularities,” which generalize Brieskorn complete intersections....

Intersection Cohomology, Monodromy, and the Milnor Fiber

We say that a complex analytic space, X is an intersection cohomology manifold if and only if the shifted constant sheaf on X is isomorphic to intersection cohomology. Given an analytic function f on an intersection cohomology manifold, we describe a simple relation between V (f) being an intersection cohomology manifold and the vanishing cycle Milnor monodromy of f . As an easy application, we...