Theta functions on the moduli space of parabolic bundles

2003/02/18 by Francesca Gavioli, Gavioli, Francesca
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG #msc:14D20 #msc:14F05 #msc:14H10 #msc:14H42

paper · pdf · doi:10.48550/arxiv.math/0302209

26 pages

arxiv created 2003/02/18 · arxiv updated 2009/11/30

Abstract

Let X be a smooth projective connected curve of genus g ≥ 2 and let I be a finite set of points of X. Fix a parabolic structure on I for rank r vector bundles on X. Let M^par denote the moduli space of parabolic semistable bundles and let L^par denote the parabolic determinant bundle. In this paper we show that the n-th tensor power line bundle L^parn on the moduli space M^par is globally generated, as soon as the integer n is such that n ≥ [(r²)/(4)]. In order to get this bound, we construct a parabolic analogue of the Quot scheme and extend the result of Popa and Roth on the estimate of its dimension.

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