Introdução à Geometria Algébrica
Data
2021-03-05
Autores
Oliveira, Luiz Filipe Moraes Saldanha 
Orientadores
Macedo, Tiago Rodrigues
Tipo
Trabalho de conclusão de curso
Título da Revista
ISSN da Revista
Título de Volume
Resumo
Geometria Algébrica é uma das mais importantes áreas da Matemática e uma das referências mais utilizadas para seu estudo é o livro “Algebraic Geometry” de Robin Hartshorne. Este livro traz uma introdução à Geometria Algébrica clássica (do ponto de vista de pontos e equações) e moderna (do ponto de vista de anéis e esquemas). O objetivo principal deste trabalho é traduzir e comentar as três primeiras seções do primeiro capítulo do livro de R. Hartshorne. Nestas seções são estudadas variedades algébricas afins e projetivas, os objetos de estudo principais da geometria algébrica clássica, além de funções regulares e morfismos de variedades. No caminho, foram estudados resultados de topologia geral e álgebra comutativa necessários para compreender o conteúdo.
Algebraic Geometry is one of the most important areas of Mathematics, and one of its most used references is the book “Algebraic Geometry” by Robin Hartshorne. This book presents an introduction to both classical Algebraic Geometry (from the point of view of points and equations) and modern (from the point of view of rings and schemes). The main goal of this work is to translate and comment the first three sections of the first chapter of this book into Portuguese. They cover the definition and initial properties of affine and projective algebraic varieties, the main objects of study classical algebraic geometry, as well as regular functions and morphisms. The material from Point Set Topology and Commutative Algebra needed to understand these first two sections is also added to the text.
Algebraic Geometry is one of the most important areas of Mathematics, and one of its most used references is the book “Algebraic Geometry” by Robin Hartshorne. This book presents an introduction to both classical Algebraic Geometry (from the point of view of points and equations) and modern (from the point of view of rings and schemes). The main goal of this work is to translate and comment the first three sections of the first chapter of this book into Portuguese. They cover the definition and initial properties of affine and projective algebraic varieties, the main objects of study classical algebraic geometry, as well as regular functions and morphisms. The material from Point Set Topology and Commutative Algebra needed to understand these first two sections is also added to the text.