**SMS scnews item created by Stephan Tillmann at Tue 20 Oct 2015 1341**

Type: Seminar

Distribution: World

Expiry: 19 Jan 2016

**Calendar1: 21 Oct 2015 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry & Topology

# A Valuation Criterion of Hironaka

### Pierre Milman (Toronto)

Wednesday 21 October 2015 from 11:00–12:00 in Carslaw 535A

Please join us for lunch after the talk!

**Abstract:**
For ideals in the rings of convergent power series expansions their
`integral closures' and, the so called, `arc-closures' coincide.
(I'll start by defining both notions.) "Integral closure contains
the arc-closure" is the nontrivial inclusion of this criterion
(first stated by H. Hironaka after which Lejeune-Teissier announced a
proof).
To prove the inclusion it
suffices to construct an ideal whose product with our ideal contains
its product with the arc-closure of our ideal. Jointly with Grant-Melles
I proved a stronger version of the latter with ideals being replaced
by coherent ideals on manifolds. (I'll explain the notion of coherency.)
Our proof (that appeared in 2006 in Ann. Fac. Sci. Toulouse Math. in
Appendix to Ch. V) is essentially an application of our algebraic
generalization of the well known Chow Theorem, i.e. that closed
complex analytic subsets of a complex projective space are algebraic.

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