Tautological systems developed in [8, 9] are Picard–Fuchs type systems to study period integrals of complete intersections in Fano varieties. We generalize tautological systems to zero loci of global sections of vector bundles. In particular, we obtain similar criterion as in [8, 9] about holonomicity and regularity of the systems. We also prove solution rank formulas and geometric realizations of solutions following the work on hypersurfaces in homogeneous varieties [4].

中文翻译：

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向量束截面和重言式系统的周期积分

在[8，9]中开发的重言式系统是Picard–Fuchs类型的系统，用于研究Fano品种中完整交集的周期积分。我们将重言式系统推广到矢量束全局截面的零位点。特别是，我们获得了与[8，9]中有关系统的完整性和规则性的相似标准。我们还研究了均质变种中超曲面的工作之后的解秩公式和解的几何实现[4]。