SINGULAR COHOMOLOGY OF THE ANALYTIC MILNOR FIBER, AND MIXED HODGE STRUCTURE ON THE NEARBY COHOMOLOGY

摘要

We describe the homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser's motivic Milnor fiber in terms of a strictly semi-stable model.