Some Special Cases of Bobadilla's Conjecture

We prove two special cases of a conjecture of J. Fernández de Bobadilla for hypersurfaces with 1-dimensional critical loci. Our approach introduces a new numerical invariant for such hypersurfaces, called the beta invariant, first defined and studied by the second author in 2014. The beta invariant is an algebraically computable invariant of the local ambient topological type of the hypersurface. We show that its vanishing is equivalent to the hypotheses of Bobadilla’s conjecture.

Topology and its Applications, Vol. 217, Pages 59–69