On the correspondence between Ulrich bundles and curves on surfaces

2025/10/15 by Bordoni, Sofia
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2510.13455

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in ℙ³.

Citations

• Ulrich bundles on a general blow--up of the plane
• On the classification of non-big Ulrich vector bundles on surfaces and\n threefolds
• An introduction to Ulrich bundles
• Stability of Rank 2 Ulrich Bundles on Projective K3 Surfaces
• Stable Ulrich bundles
• Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2)
• Resultants and Chow forms via Exterior Syzygies
• Determinantal hypersurfaces

Related

• An introduction to Ulrich bundles
• On the existence of Ulrich bundles on geometrically ruled surfaces
• On varieties with Ulrich twisted conormal bundles
• Theta divisors and Ulrich bundles on Geometrically ruled surfaces
• Ulrich bundles on surfaces with q=p_g=0