Open AccessPosted Content
Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities
TLDR
In this paper, it was shown that the Milnor number of a non-degenerate isolated complete intersection singularity is invariant to the Newton polyhedra of the component functions.Abstract:
We prove that for two germs of analytic mappings $f,g\colon (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^p,0)$ with the same Newton polyhedra which are (Khovanskii) non-degenerate and their zero sets are complete intersections with isolated singularity at the origin, there is a piecewise analytic family $\{f_t\}$ of analytic maps with $f_0=f, f_1=g$ which has a so-called {\it uniform stable radius for the Milnor fibration}. As a corollary, we show that their Milnor numbers are equal. Also, a formula for the Milnor number is given in terms of the Newton polyhedra of the component functions. This is a generalization of the result by C. Bivia-Ausina. Consequently, we obtain that the Milnor number of a non-degenerate isolated complete intersection singularity is an invariance of Newton boundaries.read more
Citations
More filters
Posted Content
Newton non-degenerate $\mu$-constant deformations admit simultaneous embedded resolutions
TL;DR: In this paper, it was shown that the family W$ is a Newton non-degenerate deformation if and only if W$ admits a simultaneous embedded resolution in the relative space of W$-jets.
Book ChapterDOI
A New Deterministic Method for Computing Milnor Number of an ICIS
TL;DR: In this article, the Milnor number of an isolated complete intersection singularity (ICIS) is considered in the context of symbolic computation and a new method for computing Milnor numbers is introduced based on the classical Le-Greuel formula.
References
More filters
Book
Singular points of complex hypersurfaces
TL;DR: The Singular Points of Complex Hypersurfaces (AM-61) as mentioned in this paper is a seminal work in the area of complex hypersurfaces, and is based on as mentioned in this paper.
Book
Isolated Singular Points on Complete Intersections
TL;DR: In this paper, the authors give a coherent account of the theory of isolated singularities of complete intersections, and show that the discriminant of the semi-universal deformation of an A-D-E singularity is isomorphic to the associated Coxeter group.
Book
Complex Geometry: An Introduction
TL;DR: Local Theory and Applications of Cohomology: Complex Manifolds, Vector Bundles, and Deformations of Complex Structures as discussed by the authors Theoretically, complex manifolds are a type of complex structures.