5 citations · 13 across the 6 of their papers we have counts for
9 papers · 1 filter
Strong Toroidalization of Birational Morphisms of 3-Folds
Steven Dale Cutkosky
In this paper we prove strong toroidalization of birational morphisms of 3-folds. Suppose that f:X\to Y is a birational morphism of nonsingular complete 3-folds, and D_Y, D_X are s…
Toroidalization of birational morphisms of 3-folds
Steven Dale Cutkosky
We prove that a birational morphism of projective 3-folds, over a field of characteristic zero, can be made toroidal by performing a sequence of blow ups of points and nonsingular…
Local monomialization of transcendental extensions
Steven Dale Cutkosky
Suppose that f is a dominant morphism from a k-variety X to a k-variety Y, where k is a field of characteristic 0 and v is a valuation of the function field k(X). We allow v to be…
Generically Finite Morphisms
Steven Dale Cutkosky
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give…
Monomialization of Morphisms From 3 Folds to Surfaces
Steven Dale Cutkosky
Suppose that is a morphism from a 3 fold to a surface (over an algebraically closed field of characteristic zero). We prove that there exist sequences of blowups of nons…
Positivity and complexity of ideal sheaves
Steven Dale Cutkosky, Lawrence Ein, Robert Lazarsfeld
The problem of bounding the "complexity" of a polynomial ideal in terms of the degrees of its generators has attracted considerable interest, brought into focus by the influential…