Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

TL;DR

This paper introduces meromorphic nearby cycle functors, explores their properties, and applies them to analyze monodromies of meromorphic functions, providing combinatorial descriptions of Hodge spectra and Jordan forms.

Contribution

It presents the first systematic study of meromorphic nearby cycle functors and their application to monodromy analysis of meromorphic functions.

Findings

Descriptions of reduced Hodge spectra

Jordan normal forms of monodromies

Functorial properties of meromorphic nearby cycle functors

Abstract

We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan normal forms will be obtained.