## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- The Japanese-Australian Workshop on Real and Complex Singularities: JARCS III. Toshizumi Fukui, Adam Harris, Alexander Isaev, Satoshi Koike and Laurentiu Paunescu, eds. Proceedings of the Centre for Mathematics and its Applications, v. 43. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2010), 141 - 174

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416321002

**Mathematical Reviews number (MathSciNet)**

MR2763241

**Zentralblatt MATH identifier**

1231.14006

#### Citation

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