Surveys in Differential Geometry

Volume 22 (2017)

Period integrals and tautological systems

Pages: 275 – 289

DOI: http://dx.doi.org/10.4310/SDG.2017.v22.n1.a10

Authors

An Huang (Department of Mathematics, Brandeis University, Waltham, Massachusetts, U.S.A.)

Bong Lian (Department of Mathematics, Brandeis University, Waltham, Massachusetts, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Chenglong Yu (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

Tautological systems are Picard–Fuchs type systems arising from varieties with large symmetry. In this survey, we discuss recent progress on the study of tautological systems. This includes tautological systems for vector bundles, a new construction of Jacobian rings for homogenous vector bundles, and relations between period integrals and zeta functions.

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Published 13 September 2018