Limits of Hodge structures via holonomic D-modules

2021/03/05 by Chen, Qianyu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.03983

Abstract

We construct the limiting mixed Hodge structure of a degeneration of compact Kähler manifolds over the unit disk with a possibly non-reduced simple normal crossing singular central fiber via holonomic \mathscr D-modules, generalizing some results of Steenbrink. Our limiting mixed Hodge structure does not carry a \mathbb Q-structure; instead, we use sesquilinear pairings on \mathscr D-modules as a replacement. The limiting mixed Hodge structure can be computed by the cohomology of the cyclic coverings of certain intersections of components of the central fiber. Additionally, we prove the local invariant cycle theorem in this setting.

Cited by

• Stratified Hyperbolicity of the moduli stack of stable minimal models, I

Related

• Variations of Mixed Hodge Structure attached to the deformation theory of a Complex Variation of Hodge Structures
• Temperate holomorphic solutions and regularity of holonomic D-modules on curves
• Three results on holonomic D-modules
• Moduli of regular holonomic D-modules with normal crossing singularities
• Limits of Hodge structures in several variables, II