Mathematical Research Letters

Volume 28 (2021)

Number 2

Period integrals of vector bundle sections and tautological systems

Pages: 415 – 434



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, University of Pennsylvania, Philadelphia, Pa., U.S.A.)


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].

B. Lian and S.-T. Yau are partially supported by the Simons Collaboration on Homological Mirror Symmetry 2015.

Received 11 May 2019

Accepted 23 December 2019

Published 13 May 2021