Browsing Department of Mathematics (MU) by Thesis Advisor "Cutkosky, Steven Dale"
Now showing items 1-6 of 6
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Algebraic resolution of formal ideals along a valuation
(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 ... -
The asymptotic Samuel function of a filtration
(University of Missouri--Columbia, 2023)We extend the asymptotic Samuel function of an ideal to an arbitrary filtration of a Noetherian ring. We observe that although many properties that hold true in the ideal case are true for filtrations, there are many ... -
Generating sequences of valuations and applications
(University of Missouri--Columbia, 2014) -
Irrational behavior of algebraic discrete valuations
(University of Missouri--Columbia, 2014)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] 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 ... -
Simultaneous local resolution along a rational valuation in two dimensional positive characteristic function fields
(University of Missouri--Columbia, 2022)We consider the condition that a germ of an algebraic mapping of nonsingular surfaces can be made finite, after sufficient blowing up along a nondiscrete rational rank 1 valuation. This problem has been solved in the ... -
Toroidalization of locally toroidal morphisms
(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 ...