A character approach to Looijenga's invariant theory for generalized root systems
A Generalization of the Milnor Number.
A Kummer-type construction of self-dual 4-manifolds.
A natural equivalence relation on singularities
A note on the discriminant of a space curve.
A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.
Ambient Deformations for Exceptional Sets in Two-Manifolds.
An explicit formula for period determinant
We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.
Appendix to : “smoothings of cusp singularities via triangle singularities”
Cohomologically insignificant degenerations
Cohomologically insignificant degenerations of algebraic varieties
Computing versal deformations.
Constant Milnor Number Implies Constant Multiplicity for Quasihomogeneous Singularities.
Coxeter elements for vanishing cycles of types and
We introduce two entire functions and in two variables. Both of them have only two critical values and , and the associated maps define topologically locally trivial fibrations over . All critical points in the singular fibers over and are ordinary double points, and the associated vanishing cycles span the middle homology group of the general fiber, whose intersection diagram forms bi-partitely decomposed infinite quivers of type and , respectively. Coxeter elements of type and...
Coxeter-Dynkin diagrams of fat points in C² and of their stabilizations.
Coxeter-Dynkin diagrams of the complete intersection singularities Z9 and Z10.
Decompositions of hypersurface singularities oftype
Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.
Deformation of Complete Intersections with Singularities.
Deformation of polar methods
We study deformations of hypersurfaces with one-dimensional singular loci by two different methods. The first method is by using the Le numbers of a hypersurfaces singularity — this falls under the general heading of a “polar” method. The second method is by studying the number of certain special types of singularities which occur in generic deformations of the original hypersurface. We compare and contrast these two methods, and provide a large number of examples.
Deformationen isolierter Kurvensingularitäten mit eingebetteten Komponenten.