Hypersurface Singularities and Milnor Equisingularity

Details Hypersurface Singularities and Milnor Equisingularity Hypersurface Singularities and Milnor Equisingularity

2005-04-19

arxiv.org/abs/math/0504380v1

Mathematics

Algebraic Geometry

A substantial improvement on our earlier paper, Hypersurface Singularities and the Swing. 15 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Hypersurface Singularities and Milnor Equisingularity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hypersurface Singularities and Milnor Equisingularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hypersurface Singularities and Milnor Equisingularity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40139