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Variations of Bridgeland stability conditions on Hirzebruch surfaces

Grant number: 17/22959-9
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): May 01, 2018
Effective date (End): January 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Marcos Benevenuto Jardim
Grantee:Valeriano Lanza
Supervisor abroad: Emanuele Macri
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: 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


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).

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