On the monodromies and the limit mixed Hodge structures of families of algebraic varieties

2016/03/02 by Takahiro Saito, Saito, Takahiro, Kiyoshi Takeuchi +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1603.00702

openalex publication_date 2016/03/02 · openalex created_date 2022/10/29 · openalex updated_date 2026/07/28

Abstract

We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we express their motivic nearby fibers in terms of the geometric data of some Newton polyhedra. In particular, the limit mixed Hodge numbers and some part of the Jordan normal forms of the monodromies of such a family will be described very explicitly.

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• Subdivisions of lower Eulerian posets and KLS theory
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