Publication
Resolution of Singularities of Germs of Curves
| Summary: | 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. |
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| Main Authors: | Canarias, Tiago Alexandre Espiga |
| Subject: | Local Analytic Geometry Puiseux Characteristics Resolution of Singularities Space Curves Blow-ups |
| Year: | 2023 |
| Country: | Portugal |
| Document type: | master thesis |
| Access type: | open access |
| Associated institution: | Universidade Nova de Lisboa |
| Language: | English |
| Origin: | Repositório Institucional da UNL |
| Summary: | 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. |
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