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Holonomic systems for period mappings. (English) Zbl 1329.57034
Summary: Period mappings were introduced in the sixties to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently to understand period integrals of algebraic manifolds. In this paper, we give an explicit construction of a tautological system for each component of a period mapping. We also show that the D-module associated with the tautological system gives rise to many interesting vanishing conditions for period integrals at certain special points of the parameter space.
MSC:
57R35 Differentiable mappings in differential topology
14J10 Families, moduli, classification: algebraic theory
53C29 Issues of holonomy in differential geometry
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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