Stability conditions on higher dimensional varieties and moduli spaces
Asymptotic and polynomial stabilities in Bridgeland stability conditions
| Full text | |
| Author(s): |
Pretti, Victor do Valle
Total Authors: 1
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| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 56, n. 1, p. 35-pg., 2025-03-01. |
| Abstract | |
We provide a systematic way of calculating the quiver region associated with a given exceptional collection. As an application, we prove that mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-stable sheaves, obtained as the cokernel of morphisms of exceptional mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-stable bundles, are Bridgeland stable, using the determinant. In the subsequent sections, we focus on the case of even rank 2 instantons over P3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}<^>3$$\end{document} and Q3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_3$$\end{document}, where we prove that instanton sheaves, instanton bundles and perverse instantons are Bridgeland stable and offer a description of the moduli space near its only actual wall. (AU) | |
| FAPESP's process: | 16/25249-0 - Bridgeland Stability and wall-crossing. |
| Grantee: | Victor Do Valle Pretti |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 19/05207-9 - Walls on Bridgeland stability conditions |
| Grantee: | Victor Do Valle Pretti |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 22/12883-3 - Quiver regions, Instantons over Fano Threefolds |
| Grantee: | Victor Do Valle Pretti |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |