Derived Categories and Fourier-Mukai Transforms

• Grant number: 23/03565-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2023
• End date: November 30, 2023
• 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 of the study of derived categories and Fourier-Mukai transforms with the objective of understanding the construction of both those objects and of their most important tools. An special focus will be given to the definition of derived categories of coherent sheaves of a scheme and their algebraic properties. As an application of the studied methods, the project will conclude with the description of Fourier-Mukai transforms between an abelian variety and its dual variety, as in the original article by Shigeru Mukai. The tools studied in this work will be of use in future studies in the area of Algebraic Geometry and Gauge Theory, specially in the study of Moduli Spaces, Bridgeland stability and instantons sheaves.