On rational maps between moduli spaces of curves and of vector bundles

2009/03/31 by Alberto Alzati, Alzati, Alberto, Michele Bolognesi +1
Mathematics · #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.0903.5515

openalex publication_date 2009/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let SU_C(2) be the moduli space of rank 2 semistable vector bundles with trivial de terminant on a smooth complex algebraic curve C of genus g > 1, we assume C non-hyperellptic if g > 2. In this paper we construct large families of pointed rational normal curves over certain linear sections of SU_C(2). This allows us to give an interpretation of these subvarieties of SUC(2) in terms of the moduli space of curves M_0,2g. In fact, there exists a natural linear map SU_C(2) -> P^g with modular meaning, whose fibers are birational to M_0,2g, the moduli space of 2g-pointed genus zero curves. If g < 4, these modular fibers are even isomorphic to the GIT compactification M^GIT_0,2g. The families of pointed rational normal curves are recovered as the fibers of the maps that classify extensions of line bundles associated to some effective divisors.

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• Rational families of vector bundles on curves, I
• Rational curves and lines on the moduli space of stable bundles
• Minimal rational curves in moduli spaces of stable bundles
• Rational Curves on Moduli Spaces of Vector Bundles
• Unirationality of the universal moduli space of semistable bundles over smooth curves