Name: Desingularization Strategies For Three-Dimensional Vector Fields (Vol. 1259)
Brand: Springer Verlag
SKU: 9783540179443
Price: 858.0 INR
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Desingularization Strategies For Three-Dimensional Vector Fields (Vol. 1259)

by Felipe Cano Torres

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ISBN13: 9783540179443
Binding: Paperback
Subject: Mathematics and Statistics
Publisher: Springer Verlag
Publisher Imprint: Springer V
Publication Date: January 16, 1987
Pages: 210
Original Price: EUR 24.99
Language: English
Edition: N/A
Item Weight: 286 grams
BISAC Subject(s): Geometry / Algebraic

About The Book

About the Book For a vector field #3, where Ai are series in X , the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2 i s, xi=x'i, i>s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the problem of reduction of singularities in characteristic p. Hence the book is potentially interesting both in the context of resolution of singularities and in that of vector fields and dynamical systems.

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