Variations of Bridgeland stability conditions on Hirzebruch surfaces

• Grant number: 17/22959-9
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: May 01, 2018
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Valeriano Lanza
• Supervisor: Emanuele Macri
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Northeastern University, United States
• Associated to the scholarship: 15/07766-4 - Moduli spaces of sheaves on Hirzebruch surfaces, Poisson geometry, and integrable systems, BP.PD

Abstract

The idea of this project consists in applying the tools of Bridgeland stability to moduli spaces of framed sheaves on Hirzebruch surfaces. In particular, three objectives are fixed: to study the chamber structure arising with the quiver description of Hilbert schemes of points of the total space of OP1(-n) (provided by the applicant in former works), to extend the already-mentioned quiver description for moduli spaces of framed sheaves on Hirzebruch surfaces to any rank, and to study more generally Bridgeland stability on Hirzebruch surfaces (a case completely open).