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| Author(s): |
Victor do Valle Pretti
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2021-09-20 |
| Examining board members: |
Marcos Benevenuto Jardim;
Abdelmoubine Amar Henni;
Daniele Faenzi;
Antony Maciocia;
Cristian Maurício Martínez Esparza
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| Advisor: | Marcos Benevenuto Jardim |
| Abstract | |
In this Ph.D. thesis, we explore local and asymptotic aspects of the theory of Bridgeland stability. The first part of the thesis is concentrated in two chapters: the first one referring to a brief discussion on the theory of schemes, derived categories and Chern characters. The second one establishes the fundamental theory of Bridgeland stability necessary for the following chapters, with a brief discussion of exceptional collections towards its end. Next, we present the main results obtained during the Ph.D. The chapter on asymptotic stability shows results analogous to the ones obtained by Jardim--Maciocia, now for objects with zero Chern character equal to zero. The last chapter is concerned with the local behavior of Bridgeland stability, describing the quiver regions on the upper-half plane of stability conditions $\mathbb{H}$ and with that proving the stability of the instantons in these regions. The thesis has an appendix and annex that discuss some intermediate theoretical and computational results obtained during the search for examples of quiver regions and their uses (AU) | |
| FAPESP's process: | 16/25249-0 - Bridgeland Stability and wall-crossing. |
| Grantee: | Victor Do Valle Pretti |
| Support Opportunities: | Scholarships in Brazil - Doctorate |