Behavior of branes under mirror symmetry in the moduli spaces of Higgs bundles
Boundary of the moduli space of instanton bundles on projective space
Moduli spaces of pfaffian representations of cubic three-folds and instanton bundles
| Full text | |
| Author(s): |
Liu, Wanmin
;
Lo, Jason
;
Martinez, Cristian
Total Authors: 3
|
| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 55, n. 4, p. 38-pg., 2024-12-01. |
| Abstract | |
On a Weierstra ss elliptic surface X, we define a "limit" of Bridgeland stability conditions, denoted as Zl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z<^>l$$\end{document}-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a Zl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z<^>l$$\end{document}-stable object, and describe a modification upon which a Zl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z<^>l$$\end{document}-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf. We also study wall-crossing for Bridgeland stability, and show that 1-dimensional twisted Gieseker semistable sheaves are taken by a Fourier-Mukai transform to Bridgeland semistable objects. (AU) | |
| FAPESP's process: | 18/21391-1 - Gauge theory and algebraic geometry |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/06938-4 - Geometry of moduli spaces of sheaves via wall-crossing |
| Grantee: | Cristian Mauricio Martinez Esparza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |