Schemes and algebraic varieties

• Grant number: 20/16173-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2021
• End date: January 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Guido Neulaender
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM

Abstract

This project will consist in the study of Algebraic Varieties and Schemes with the intention of characterizing both objects and understanding the relationship between them. A special attention will be given to the schemes that cannot be represented with a variety structure, aiming to comprehend the advantages of the more modern definition compared to the classic one. During the course of the project, requirements for the study of the subject, such as Homological Algebra and Commutative Algebra, will also be discussed, as these concepts provide the foundation necessary, in addition to Schemes, for the research of more advanced topics in Algebraic Geometry, such as Sheaves and Moduli Spaces. Moreover, this project research will culminate in the writing of an introductory text for undergraduate students, with the intention of providing free and accessible notes for those interested in research on Algebraic Geometry.