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math.AC2012
A refinement of Izumi's Theorem
Sébastien Boucksom, Charles Favre, Mattias Jonsson
We improve Izumi's inequality, which states that any divisorial valuation v centered at a closed point 0 on an algebraic variety Y is controlled by the order of vanishing at 0. Mor…
math.AC2002
The valuative tree
Charles Favre, Mattias Jonsson
We describe the set V of all real valued valuations v on the ring C[[x,y]] normalized by min{v(x),v(y)}=1. It has a natural structure of an R-tree, induced by the order relation v…