On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve

2012/08/03 by L. Brambila‐Paz, L. Brambila-Paz, Brambila-Paz, L. +2
Mathematics · #14H60 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14H60 #msc:14J60

paper · pdf · doi:10.48550/arxiv.1208.0869

Typos corrected and minor style changes, no mathematical changes. Final version to appear in Manuscripta Mathematica

openalex publication_date 2012/08/03 · arxiv created 2013/03/28 · arxiv updated 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M(n,ξ) be the moduli space of stable vector bundles of rank n≥ 3 and fixed determinant ξ over a smooth projective algebraic curve X over ℂ of genus g≥ 4. We use the gonality of the curve and r-Hecke morphisms to describe a smooth open set and to compute the dimension of a component of the Hilbert scheme Hilb_M(n,ξ), of the scheme of morphisms Mor(\mathbbG,M(n,ξ)) and of the moduli space M_X × \mathbbG of stable bundles over X× \mathbbG, where \mathbbG is the Grassmannian \mathbbG(n-r,ℂⁿ). In particular, we prove that dim Mor_P(ℙ²,M(3,ξ))=8g-7 and we give a sufficient condition for Mor_2ns(ℙ¹,M(n,ξ)) to be non-empty with s≥ 1.

Citations

• On (k,l)-stable vector bundles over algebraic curves

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