**SMS scnews item created by Stephan Tillmann at Sun 14 Sep 2014 1121**

Type: Seminar

Distribution: World

Expiry: 14 Dec 2014

**Calendar1: 17 Sep 2014 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry-Topology-Analysis Seminar

# Finiteness on semialgebraic types of Nash mappings defined on a Nash surface

### Satoshi Koike

GTA Seminar - Wednesday, 17 September, 11:00-12:00 in Carlaw 535A

Please join us for lunch after the talk!

##
Finiteness on semialgebraic types of Nash mappings defined on a Nash surface

Satoshi Koike (Hyogo)

We consider a problem on whether the number
of semialgebraic types appearing in a family of Nash mappings
defined on a 2-dimensional Nash surface is finite.
We show that if the Nash surface has isolated singularities,
then the number is finite.
On the other hand, we show that if it has non-isolated
singularities, namely its singular locus is one-dimensional,
then the number can be infinite.
We give such a negative example in the algebraic case.
This is a joint work with Masahiro Shiota.