Lower estimate of Milnor number and characterization of isolated homogeneous hypersurface singularities

Moduli of Isolated Hypersurface Singularities

It was shown by J.N. Mather and S.S.-T. Yau that an isolated complex hypersurface singularity is completely determined by its moduli algebra. In this article it is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and, hence, associate invariants to the singularities themselves.

Equivalences between isolated hypersurface singularities

Let (9,+1 be the ring of germs of holomorphic functions (C ~+ 1, 0 ) ~ C. There are many important equivalence relations that have been defined on the elements of (9+ 1. ~ ' , ~s and ~f-equivalence are well known in function theory. Each of these equivalence relations can be defined in terms of a Lie group action on (9 +1For instance two functions are defined to be ~-equivalent if they are the ...

Milnor Number of Weighted-Lê–Yomdin Singularities

Continuous Invariants of Isolated Hypersurface Singularities

is a finite-dimensional algebra depending only on the germ of V at the origin and is invariant under holomorphic change of coördinates. Remarkably, it was shown by Mather and Yau [4] that A completely determines the germ of V . Thus, one should be able to distinguish between biholomorphically inequivalent singularities on the basis of their corresponding moduli algebras. This was accomplished f...

Non-isolated Hypersurface Singularities and Lê Cycles

In this series of lectures, I will discuss results for complex hypersurfaces with non-isolated singularities. In Lecture 1, I will review basic definitions and results on complex hypersurfaces, and then present classical material on the Milnor fiber and fibration. In Lecture 2, I will present basic results from Morse theory, and use them to prove some results about complex hypersurfaces, includ...