The Valuative Tree

• Main Authors: Favre, Charles (Author, http://id.loc.gov/vocabulary/relators/aut), Jonsson, Mattias (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1853
• Subjects: Discrete mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Topology.; Discrete Mathematics.; Algebraic Geometry.; Commutative Rings and Algebras.
• Physical Description: XVI, 244 p. online resource.
• ISBN: 9783540446460
• ISSN: 0075-8434 ;
• DOI: 10.1007/b100262

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.