Building on work of the fourth author and Morelli's work, we prove the weak factorization
conjecture for birational maps in characteristic zero: a birational map between complete …

The purpose of this article and of" Resolution of singularities of threefolds in positive
characteristic II" is to prove the theorem of resolution: resolution of singularities holds for …

The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of
singularities by simple algebraic mappings is truly a fundamental problem. It has a complete …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

We classify all possible extensions of a valuation from a ground field $ K $ to a rational
function field in one or several variables over $ K $. We determine which value groups and …

I shall sketch a brief history of the desingularization problem from Riemann thru Zariski to
Hironaka, including the part I played in it and the work on Galois theory which this led me to …

A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally
be represented in e'tale neighborhoods by a pure monomial mappings. The book gives …

Given an ideal I on a variety X with toroidal singularities, we produce a modification X→ X,
functorial for toroidal morphisms, making the ideal monomial on a toroidal stack X. We do …

The Curves The Point of View of Max Noether Probably the oldest references to the problem
of resolution of singularities are found in Max Noether's works on plane curves …

Local monomialization of transcendental extensions Page 1 ANNA L E S D E L’INSTITU T
FO U RIER ANNALES DE L’INSTITUT FOURIER Steven Dale CUTKOSKY Local …