5 citations · 13 across the 6 of their papers we have counts for
7 papers
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…
Asymptotic behaviour of the length of local cohomology
Steven Dale Cutkosky, Huy Tai Ha, Hema Srinivasan +1
Let k be a field of characteristic 0, R = k[x_1, ..., x_d] be a polynomial ring, and m its maximal homogeneous ideal. Let I be a homogeneous ideal in R. In this paper we investigat…
Completions of valuation rings
Steven Dale Cutkosky, Laura Ghezzi
Let k be a field of characteristic zero, K an algebraic function field over k, and V a k-valuation ring of K. Zariski's theorem of local uniformization shows that there exist algeb…
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…
Arithmetic Macaulayfication of projective schemes
S. D. Cutkosky, Huy Tai Ha
In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. We give a necessary and sufficient condition for a nonsingular projective sch…