Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)
Tat Thang Nguyen, Kiyoshi Takeuchi

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Advanced Combinatorial Mathematics
