Advanced search
Free plane algebraic curves
Full text
| |
| Author(s): |
Cibele Carolina de Souza Sá
Total Authors: 1
|
| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2024-03-07 |
| Examining board members: |
Marcos Benevenuto Jardim;
Zaqueu Alves Ramos;
Alan do Nascimento Muniz
|
| Advisor: | Marcos Benevenuto Jardim |
| Abstract | |
In this work, we will present the concepts and some classical characterizations of the freeness of algebraic plane curves, a study that began in the 1980s by the Japanese mathematician Kyoji Saito. We will first discuss some concepts of Commutative Algebra such as regular sequences, homological dimension, depth, the Hilbert-Burch theorem and the Auslander-Buchsbaum theorem. We will also take a brief look into algebraic plane curves. Next, we will deal with the main topic of this dissertation: derivations, focusing on the Saito's module of a homogeneous polynomial. We will see here that a divisor is said to be free when this module is free over a graded ring of polynomials. In addition, some freeness criteria and examples applying each of them will be presented. Finally, we will present an important numerical invariant, the Bourbaki degree of plane curves, which is an excellent tool for testing the non-freeness of curves (AU) | |
| FAPESP's process: | 22/03283-2 - Free plane algebraic curves |
| Grantee: | Cibele Carolina de Souza Sá |
| Support Opportunities: | Scholarships in Brazil - Master |