The Valuative Tree

Download or read book The Valuative Tree written by Charles Favre and published by Springer. This book was released on 2004-08-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.