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Derived Categories and Fourier-Mukai Transforms

Grant number: 23/03565-0
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): May 01, 2023
Effective date (End): 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.

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