Contact loci, motivic Milnor fibers of nondegenerate singularities

Abstract

: Inspired by Denef-Loeser’s identity of the Euler characteristic with compact supports of the contact loci with the Lefschetz numbers of a complex singularity, we study sheaf cohomology groups of contact loci of complex nondegenerate singularities. Moreover, also for these singularities, we obtain a motivic analogue of Leˆ Du˜ng Tra´ng’s work on a monodromy relation of a complex singularity and its restriction to a generic hyperplane.