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Desingularization Strategies of Three-Dimensional Vector Fields (Paperback, 1987 ed.)
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Desingularization Strategies of Three-Dimensional Vector Fields (Paperback, 1987 ed.)
Series: Lecture Notes in Mathematics, 1259
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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>i"/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.
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Lecture Notes in Mathematics, 1259 |
Release date: |
May 1987 |
First published: |
1987 |
Authors: |
Felipe Cano Torres
|
Dimensions: |
235 x 155 x 10mm (L x W x T) |
Format: |
Paperback
|
Pages: |
192 |
Edition: |
1987 ed. |
ISBN-13: |
978-3-540-17944-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Algebraic geometry
|
LSN: |
3-540-17944-5 |
Barcode: |
9783540179443 |
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