The irreducibility of the moduli space of stable vector bundles of rank 2 on a quintic in \pp³

1995/03/22 by Pieter G.J Nijsse, Nijsse, Pieter · 2 citations
Mathematics · #14D20 (Primary) 14J29 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9503012

openalex publication_date 1995/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper I consider a quintic surface in \pp³, general in the sense of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which are μ-stable with respect to the hyperplane section and have c₁ = K, the canonical class of the surface and fixed c₂, are parametrized by a moduli space. This space is known to be irreducible for large c₂ (work of K.G. O'Grady). I give an explicit bound, namely c₂ ≥ 16.

Cited by

• Irreducibility of moduli of vector bundles over a very general sextic Surface
• Vector bundles on bielliptic surfaces: Ulrich bundles and degree of irrationality

Related

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• Rank-3 stable bundles on rational ruled surfaces
• Irreducibility of moduli of vector bundles over a very general sextic Surface
• Irreducibility of moduli spaces of vector bundles on K3 surfaces
• Disconnected moduli spaces of stable bundles on surfaces