椭圆纤维化的主丛
Principal bundles on elliptic fibrations
摘要：
在最近的研究F-理论和杂种弦的对偶性中，具有各种结构群G的主丛的模在一个椭圆纤维的卡-丘流形上起着核心作用，在这个流形上杂种理论是紧的。本文提出一种简单的代数几何方法来研究基S上椭圆纤维化的任意簇X上的主G-丛的模空间：模空间本身在S的谱覆盖$\tilde{S}$参数化的加权射影基上自然纤维化，而纤维被确定为这些覆盖的特殊Prym的平移.在好的情况下，一般的Prym纤维是一个有限群和$Pic(\tilde{S})$的一个交换子簇的乘积的同构。
英文摘要：
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic theory is compactified. In this note we propose a simple algebro-geometric technique for studying the moduli spaces of principal G-bundles on an arbitrary variety X which is elliptically fibered over a base S: The moduli space itself is naturally fibered over a weighted projective base parametrizing spectral covers $\tilde{S}$ of S, and the fibers are identified as translates of distinguished Pryms of these covers. In nice situations, the generic Prym fiber is isogenous to the product of a finite group and an abelian subvariety of $Pic(\tilde{S})$.
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