On the quiver descriptions of Hilbert and Quot schemes and beyond

• Grant number: 24/05296-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2024
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Pedro Henrique dos Santos
• 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

Hilbert and Quot schemes are quite important in modern Algebraic Geometry, asthey have an important role in such areas as the construction of moduli spaces anddeformation theory. When working with Hilbert schemes of points, it is quite clear thatthe difficulty of the problems increases quite fast with the dimension of the space andthe number of points, so that any kind of generalization may be quite hard. The presentproject was conceived thinking of proceeding in two different directions. The first isstill related to my thesis and the quiver theory linked to Hilbert schemes of points. Theother is about different topics, in some way related to the first, but with approachespotentially not connected with quivers. I think it is indeed important to make contactwith different topics and techniques, with a view to improve as a researcher. (AU)