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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.
Supplementary Materials