## Proceedings of the Centre for Mathematics and its Applications

### Monodromies at Infinity of Polynomial Maps and $A$-hypergeometric Functions

Kiyoshi Takeuchi

#### Abstract

We review our recent results on monodromies at infinity of polynomial maps and $A$-hypergeometric functions. By using the theory of mixed Hodge modules, we introduce motivic global Milnor fibers of polynomial maps which encode the information of their monodromies at infinity into mixed Hodge structures with finite group actions. The numbers of the Jordan blocks in the monodromy at infinity of the polynomial will be described by its Newton polyhedron at infinity

#### Article information

Dates
First available in Project Euclid: 18 November 2014

Takeuchi, Kiyoshi. Monodromies at Infinity of Polynomial Maps and $A$-hypergeometric Functions. The Japanese-Australian Workshop on Real and Complex Singularities: JARCS III, 141--174, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2010. https://projecteuclid.org/euclid.pcma/1416321002