Stability conditions on higher dimensional varieties and boundedness for Bridgeland walls for one dimensional classes on P3

• Grant number: 23/06829-9
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: December 01, 2023
• End date: November 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Dapeng Mu
• Supervisor: Antony Maciocia
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Edinburgh, Scotland
• Associated to the scholarship: 20/03499-0 - Stability conditions on higher dimensional varieties and moduli spaces, BP.PD

Abstract

I am planning to work on two projects on stability conditions, which are both following my Ph.D. work. The first one is to generalize the Euler stability in my thesis to other varieties, especially the ones with strong exceptional collections. Currently, the most common construction is by tilting the heart,which becomes too complicated to handle on a variety with dimensions greater than 3. Our approach avoids the study of all the intermediate tilts, and it may shed some light on a new method to construct stability conditions. The second project is to prove that Bridgeland walls for any one-dimensional class on P3 are bounded. I partially proved it in my thesis, and I hope to prove it completely. Walls on a threefold are much harder to work with than on a surface. So far, there has been work on asymptotic stability on a threefold for any class. I am aiming at proving a stronger result that walls are bounded, but with the focus only on the easiest case, a one-dimensional class. (AU)