Excess dimensions of Brill--Noether schemes of rank two stable bundles

2022/10/23 by Ali Bajravani, Bajravani, Ali
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2210.12764

openalex publication_date 2022/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use results of M. Aprodu and E. Sernesi to extend a result by Fulton--Harris--Lazarsfeld in Brill--Noether theory of line bundles %and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to Brill--Noether loci of stable bundles inside the moduli space of rank two stable vector bundles on a smooth projective algebraic curve. As a consequence; if B^k_{2, d} is of expected dimension, then we prove that its smoothness is equivalent with the smoothness of B^k_{2, d+1}.

Related

• Excess dimensions for Brill-Noether schemes of stable vector bundles
• Brill--Noether loci of stable rank--two vector bundles on a general curve
• Martens and Mumford theorems for higher rank Brill--Noether loci
• Brill--Noether loci on moduli spaces of symplectic bundles over curves
• Brill-Noether loci of rank two vector bundles on a general ν-gonal curve