On the local uniformization of Abhyankar valuations using toric maps
Presenter
May 7, 2013
Keywords:
- characteristic p
- commutative algebra
- birational algebraic geometry
- multiplier ideals
- singularities of varieties
- valuation rings
- toric maps
MSC:
- 13A35
- 13A15
- 13A18
- 13Axx
- 13-xx
- 14-xx
- 14Exx
- 14E05
- 14E15
Abstract
We will study valuations on an excellent Noetherian local domain R which are such that the inclusion R \subset R_v in the valuation induces a trivial residue field extension with the rational rank of the value group equal to the dimension of R. Assuming that the residue field R/m is algebraically closed we will give an overview of their local uniformization and stress the fact that not only are they quasi-monomial, but they are toroidal in nature: the valuation ring is the limit of a nested system of birational toric maps between regular local rings.