Purity of the branch locus and Lefschetz theorems
Symbolic algebras of monomial primes.
On Fano 3-Folds.
On unique and almost unique factorization of complete ideals II.
A new characterization of rational surface singularities.
A simpler proof of toroidalization of morphisms from 3-folds to surfaces
We give a simpler and more conceptual proof of toroidalization of morphisms of 3-folds to surfaces, over an algebraically closed field of characteristic zero. A toroidalization is obtained by performing sequences of blow ups of nonsingular subvarieties above the domain and range, to make a morphism toroidal. The original proof of toroidalization of morphisms of 3-folds to surfaces is much more complicated.
Local monomialization of transcendental extensions
Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.
Formal prime ideals of infinite value and their algebraic resolution
Suppose that is a local domain essentially of finite type over a field of characteristic , and a valuation of the quotient field of which dominates . The rank of such a valuation often increases upon extending the valuation to a valuation dominating , the completion of . When the rank of is , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than , there is no natural ideal in that...
Page 1