Let X be a smooth projective connected curve of genus $g \ge 2$ and let I bea finite set of points of X. Fix a parabolic structure on I for rank r vectorbundles on X. Let $M^{par}$ denote the moduli space of parabolic semistablebundles and let $L^{par}$ denote the parabolic determinant bundle. In thispaper we show that the n-th tensor power line bundle ${L^{par}}^n$ on themoduli space $M^{par}$ is globally generated, as soon as the integer n is suchthat $n \ge [\frac{r^2}{4}]$. In order to get this bound, we construct aparabolic analogue of the Quot scheme and extend the result of Popa and Roth onthe estimate of its dimension.
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机译：令X为$ g \ ge 2 $族的光滑投影连通曲线，令I为X的有限点集。为X上的秩r向量束在I上固定抛物线结构。令$ M ^ {par} $表示抛物半稳定束的模空间，并令$ L ^ {par} $表示抛物行列式束。在本文中，我们表明模数空间$ M ^ {par} $上的第n个张量电源线束$ {L ^ {par}} ^ n $是全局生成的，只要整数n为$ n \ ge [\ frac {r ^ 2} {4}] $。为了达到这个界限，我们构造了Quot方案的抛物线类似物，并在其尺寸估计上扩展了Popa和Roth的结果。
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