A New Conjecture, a New Invariant, and a New Non-splitting Result
Algebraic Geometry
2015-04-28 v4
Abstract
We prove a new non-splitting result for the cohomology of the Milnor fiber, reminiscent of the classical result proved independently by Lazzeri, Gabrielov, and L\^e in 1973-74. We do this while exploring a conjecture of Bobadilla about a stronger version of our non-splitting result. To explore this conjecture, we define a new numerical invariant for hypersurfaces with -dimensional critical loci: the beta invariant. The beta invariant is an invariant of the ambient topological-type of the hypersurface, is non-negative, and is algebraically calculable. Results about the beta invariant remove the topology from Bobadilla's conjecture and turn it into a purely algebraic question.
Keywords
Cite
@article{arxiv.1410.3316,
title = {A New Conjecture, a New Invariant, and a New Non-splitting Result},
author = {David B. Massey},
journal= {arXiv preprint arXiv:1410.3316},
year = {2015}
}