Rational families of vector bundles on curves, I

2003/02/12 by Ana-Maria Castravet, Castravet, Ana-Maria
Mathematics · #14Exx (Secondary) #14H60 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14Exx #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0302133

23 pages

arxiv created 2003/02/12 · openalex publication_date 2003/02/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth complex projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k>1, we find two irreducible components of the space of rational curves of degree k on M. One component, which we call the nice component has the property that the general element is a very free curve if k is sufficiently large. The other component has the general element a free curve. Both components have the expected dimension and their maximal rationally connected fibration is the Jacobian of the curve C.

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