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

2020/11/02 by Fujisawa, Taro
#14A21 #14C30 #32S35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.00926

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 nilpotnet orbit in several variables.

Related

• Limits of Hodge structures in several variables, II
• Mixed Hodge structures in log symplectic geometry
• Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic p>0 and log weak Lefschetz conjecture for log crystalline cohomologies
• Classifying spaces of degenerating mixed Hodge structures, VI: Log real analytic functions and log C^∞ functions
• Deligne--Beilinson cohomology and log Hodge theory