The Brill-Noether Theory of the Moduli Spaces of Sheaves on Surfaces

2023/06/19 by İzzet Coşkun, Jack Huizenga, Coskun, Izzet +3 · 1 citation
Mathematics · #14M15 #14M17. Secondary: 14L35 #51N30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Primary: 14L30

paper · pdf · doi:10.48550/arxiv.2306.11033

openalex publication_date 2023/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we survey recent developments in the Brill-Noether Theory of higher rank vector bundles on complex projective surfaces. We focus on weak Brill-Noether Theorems on rational and K-trivial surfaces and their applications.

Cited by

• Higher rank Clifford's theorem on the smooth quadric

Related

• Weak Brill-Noether for rational surfaces
• On the Brill-Noether theory for K3 surfaces
• Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
• Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves
• Brill-Noether theory on the projective plane for bundles with many sections