Action of derived equivalences on Bridgeland stability conditions over threefolds

• Grant number: 25/02221-1
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: July 01, 2025
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eduardo do Nascimento Marcos
• Grantee: Victor Do Valle Pretti
• Supervisor: Jason Lo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: California State University, Northridge, United States
• Associated to the scholarship: 22/12883-3 - Quiver regions, Instantons over Fano Threefolds, BP.PD

Abstract

The objective of this project is to study the possible hearts of t-structures that can be used for a Bridgeland stability condition on a smooth projective three-dimensional variety. Understanding this is central to studying the action of automorphisms of the derived category on the moduli space of Bridgeland stable objects, resulting in a deeper understanding of the geometry of these spaces. Furthermore, we aim to use this study to comprehend the structure of the space of Bridgeland stability conditions in the context of three-dimensional varieties, which is still underdeveloped in the literature.