Modular subvarieties and birational geometry of SU_C(r)

2010/02/23 by Michele Bolognesi, Bolognesi, Michele, Sonia Brivio +1
Mathematics · #14H10 #14H60 #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.1002.4382

openalex publication_date 2010/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be an algebraic smooth complex genus g>1 curve. The object of this paper is the study of the birational structure of the coarse moduli space U_C(r,0) of semi-stable rank r vector bundles on C with degree 0 determinant and of its moduli subspace SU_C(r) given by the vector bundles with trivial determinant. Notably we prove that U_C(r,0) (resp. SU_C(r)) is birational to a fibration over the symmetric product C^(rg) (resp. over P^(r-1)g) whose fibres are GIT quotients (P^r-1)^rg//PGL(r). In the cases of low rank and genus our construction produces families of classical modular varieties contained in the Coble hypersurfaces.

Citations

• The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian

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