Limiting mixed Hodge structures on the relative log de Rham cohomology groups of a projective semistable log smooth degeneration

Abstract

We prove that the relative log de Rham cohomology groups of a projective semistable log smooth degeneration admit a natural limiting mixed Hodge structure. More precisely, we construct a family of increasing filtrations and a family of nilpotent endomorphisms on the relative log de Rham cohomology groups and show that they satisfy a part of good properties of a nilpotent orbit in several variables.