Year: 2005
Type: preprint
Abstract: Suppose that $f$ defines a singular, complex affine hypersurface. If the critical locus of $f$ is one-dimensional at the origin, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber, $F_{f, \mathbf 0}$, of $f$ at the origin, with either integral or $\mathbb Z/p\mathbb Z$ coefficients. If the critical locus of $f$ has arbitrary dimension, we show that the smallest possibly non-zero reduced Betti number of $F_{f, \mathbf 0}$ completely determines if $f$ defines a family of isolated singularities, over a smooth base, with constant Milnor number. This result has a nice interpretation in terms of the structure of the vanishing cycles as an object in the perverse category.
Source: arXiv (Cornell University)
Authors: Tráng, Lê Dũng, Massey, David B.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2016194965