We study period integrals of CY hypersurfaces in a partial flag variety. We construct a regular holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations has lead us to the notion of a tautological system.
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Bong H. Lian, Ruifang Song, Shing-Tung Yau, Periodic integrals and tautological systems. J. Eur. Math. Soc. 15 (2013), no. 4, pp. 1457–1483DOI 10.4171/JEMS/396