Theta functions on the moduli space of parabolic bundles

Details Theta functions on the moduli space of parabolic bundles Theta functions on the moduli space of parabolic bundles

2003-02-18

arxiv.org/abs/math/0302209v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

Let X be a smooth projective connected curve of genus $g \ge 2$ 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 ${L^{par}}^n$ on the moduli space $M^{par}$ is globally generated, as soon as the integer n is such that $n \ge [\frac{r^2}{4}]$. 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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