Bridgeland Stability on Projective Varieties

• Grant number: 23/15556-6
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2024
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Agreement: ANR
• 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: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

This project seeks to contribute to the study of Bridgeland stability conditions, first introduced by Bridgeland in 2002, on smooth projective three-fold, whose case is still lacking in the current literature. A special focus is given to the problem of finding stability conditions on the blow-up of the projective space over smooth curves, following the 2019 work by Martinez-Schmidt-Das for the blow-up over a point; as well as the geometric study of the complex variety associated with Bridgeland stability conditions for Fano varieties of Picard rank 1 and 2 by the tool of asymptotic stability, expanding the results established in the recent work by Jardim-Maciocia and Jardim-Maciocia-Martinez for Picard rank 1.