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)

# A Valuation Criterion of Hironaka

### Pierre Milman (Toronto)

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

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.