Valuative invariants of singularities
by
Antonio Campillo
Valladolid

Looking to valuations canonically associated a singularity (for instance essential valuations, arc spaces valuations or Rees valuations of the jacobian ideal) one can get invariants for the singularities by several objets asociatel to such valuations or sets of them. Particulary, we introduce the Arf closure relative to finitely many valuations. Arf closure becames a commutative algebra technique which gives the information of the image on the singularity of smooth curves transversal to divisorial centers of the valuation. Thus one gets and algebric-geometric theory of invariants of singularities coming from the geometry of special arcs on it. When applied to Rees valuations of the jacobian ideal one gets invariants type the polar invariants of the singularities.

Date received: April 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-39.