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New & Forthcoming Titles | The Valuative Tree

The Valuative Tree

Series: Lecture Notes in Mathematics, Vol. 1853

Favre, Charles, Jonsson, Mattias

2004, XVI, 244 p.

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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.

Content Level » Research

Keywords » Graph - Laplace operator - Riemann-Zariski surface - Zariski topology - classification - dual graphs - trees - valuations

Related subjects » Algebra - Geometry & Topology

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