Moduli spaces of stable bundles on ruled 3-folds and Brill-Noether problems

2025/07/09 by Costa, Laura, Tarrío, Irene Macías
#14J30 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.06882

Abstract

In this paper, we redefine the theory of walls and chambers due to Qin developing a new tool to study moduli spaces of stable rank 2 vector bundles on algebraic varieties of higher dimension. We apply it to describe components of some moduli spaces of rank 2 stable bundles on ruled 3-folds as well as to prove that some Brill-Noether loci are non-empty.

Citations

• Brill-Noether Theory of stable vector bundles on ruled surfaces
• Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
• A home-made Hartshorne-Serre correspondence
• On Stable Bundles of Ranks 2 and 3 on P³

Related

• Brill-Noether Theory of stable vector bundles on ruled surfaces
• Excess dimensions of Brill--Noether schemes of rank two stable bundles
• Moduli of Stable Sheaves on a Smooth Quadric in \PP₃
• A note on the Brill-Noether loci of small codimension in moduli space of stable bundles
• Excess dimensions for Brill-Noether schemes of stable vector bundles