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Resolution of Singularities of Germs of Curves
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| 1.72 MB | Adobe PDF |
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Resumo(s)
Our main goal in this work is to introduce the reader to a subarea of algebraic geometry
known as local analytic geometry. In this thesis we will give some general concepts,
going in depth into the study of irreducible curves and giving algorithms in the computer
program SINGULAR for the computation of the examples presented in this thesis. Most
of the work will use a well-known mathematical object called Puiseux series, a tool that
allows us to parameterize analytic curves locally, hence its importance for the resolution
of singularities. This work provides a detailed description of how Puiseux characteristics
evolve after a finite number of blow-ups.
Descrição
Palavras-chave
Local Analytic Geometry Puiseux Characteristics Resolution of Singularities Space Curves Blow-ups