New Period Mappings for Plane Curve Singularities

1998/02/02 by Rainer Kaenders, Rainer H. Kaenders, Kaenders, Rainer H. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG #math.CV #msc:14B05 #msc:14F35 #msc:14H20 #msc:32S35

paper · pdf · doi:10.48550/arxiv.math/9802011

75 pages, LaTeX2e; the same paper! By accident the documentclass of Trans. Amer. Math. Soc. had been used in the first version

arxiv created 1998/02/05 · arxiv updated 2009/11/30

Abstract

For plane curve singularities we construct a mixed Hodge structure (MHS) over the integers on the fundamental group of the Milnor fiber. The concept nearby fundamental group is introduced and we develop a theory of iterated integrals along elements of this group. We give an example for which the MHS on the nearby fundamental group detects a modulus which is invisible for the MHS on the vanishing cohomology.

Cited by

• Periods of Limit Mixed Hodge Structures

Related

• Deformation Theory and Limiting Mixed Hodge Structures
• Spectrum of Projective Plane Curve Arrangements with Ordinary Singularities
• Motivic Milnor fibers of plane curve singularities
• Period integrals and Hodge modules
• Combinatorial aspects of the mixed Hodge structure