Period Integrals and Tautological Systems
Student No.:50
Time:Mon./Wed. 10:10-12:00
Instructor:Bong Lian  [Brandeis University]
Place:Lecture Hall, Floor 3, Jin Chun Yuan West Building; Place move to Seminar Room, third floor from July 2.
Starting Date:2012-6-4
Ending Date:2012-8-6



Time: change to Mon./Wed. 13:00-14:50 on June 4 and 6;

           lectures move to Wed./Fri. in week of June 11 and July 9


 Place: move to Seminar Room, Third Floor from July 2.


Course description:

We develop a global residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. Two important ingredients of this construction are the notion of a CY principal bundle, and a classification of such rank one bundles.

We also generalize the construction to CY and general type complete intersections. When $X$ is an algebraic manifold having a sufficiently large automorphism group $G$ and $V^*$ is a linear representation of $G$, we construct a holonomic D-module that governs the period integrals.



Basic knowledge of complex geometry and graduate level algebra.


Reference for the course:

B.H. Lian, R. Song and S.-T. Yau, {\it Period Integrals and Tautological Systems}, arXiv:1105.2984v1.

B.H. Lian and S.-T. Yau, {\it Period Integrals of CY and General Type Complete Intersections}, arXiv:1105.4872v3, to appear in InventionaeMathematicae 2012-2013.