Rank-Two Reflexive Sheaves on the Projective Space with Second Chern Class Equal to Four

Author(s)

Jardim, Marcos ; Muniz, Alan

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 56, n. 2, p. 53-pg., 2025-06-01.

Abstract

We study rank-two reflexive sheaves on 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} with c2=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_2 =4$$\end{document}, expanding on previous results for c2 <= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_2\le 3$$\end{document}. We show that every spectrum not previously ruled out is realized. Moreover, moduli spaces are studied and described in detail for c1=-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_1=-1$$\end{document} or 0 and c3 >= 8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_3\ge 8$$\end{document}. (AU)

• FAPESP's process: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability
• Grantee: Henrique Nogueira de Sá Earp
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/21391-1 - Gauge theory and algebraic geometry
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Research Projects - Thematic Grants