A New Conjecture, a New Invariant, and a New Non-splitting Result
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 Lê 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 $1$-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- arXiv:
- arXiv:1410.3316
- Bibcode:
- 2014arXiv1410.3316M
- Keywords:
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- Mathematics - Algebraic Geometry;
- 32B15;
- 32C35;
- 32C18;
- 32B10