Program
 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

NOTICE:

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.

Prerequisite:

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.