Seminario de Álgebra

S. Dale Cutkosky

(University of Missouri)

"Extension under projection of associated graded rings along a valuation"

Lunes 5 de junio de 2017 a las 12:30 horas en el aula 420 del módulo 17

Resumen: A central method in resolution of singularities is to take a finite projection to a regular variety, and then to make a local analysis of the ramification of this projection to understand which blow ups are required to improve the singularity. In local uniformization, this analysis is made along a fixed, arbitrary  valuation, so it can be very complicated (the value group may not be finitely generated).

The relevant information about this projection, and the effect of the possible blow ups along the valuation, is captured in the extension of associated graded rings along the valuation. The associated graded ring along a valuation was introduced by Teissier; it is central in his work on local uniformization in positive characteristic.

In this talk we define the associated graded ring along the valuation, and consider the structure of the extension of associated graded rings along a  projection, and stable forms of the extension after sufficient blowing up along the valuation.