• Algebraic resolution of formal ideals along a valuation 

    El Hitti, Samar, 1979- (University of Missouri--Columbia, 2008)
    Let X be a possibly singular complete algebraic variety, defined over a field [kappa] of characteristic zero. X is nonsingular at [rho] [element of] X if OX,[rho] is a regular local ring. The problem of resolution of ...
  • Irrational behavior of algebraic discrete valuations 

    Sanyal, Soumya Deepta ([University of Missouri--Columbia], 2014)
    We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities ...
  • Toroidalization of locally toroidal morphisms 

    Hanumanthu, Krishna Chaithanya, 1981- (University of Missouri--Columbia, 2008)
    Let X and Y be nonsingular varieties over an algebraically closed field [kappa] of characteristic zero. A toroidal structure on X is a simple normal crossing divisor DX on X. Suppose that DX and DY are toroidal structures ...