Tautological Systems and Poincare Residue Formula (I): General Theory


Tsung-Ju Lee ( National Taiwan University )
2015-04-10  09:10 - 11:00
Room 101, Mathematics Research Center Building (ori. New Math. Bldg.)

The GKZ-system is too “small” to determine the full (polynomial) moduli space of CY hypersurfaces in the given toric variety $X$ in general. One way to modify this is to consider the full symmetry group, i.e., $\aut(X)$. This was introduced by B. Lian and S.-T. Yau, which is nowadays called the tautological system. The tautological system can be even defined in a more general setting, e.g. a $G$-equivariant principal $H$-bundle $H-M\to X$ over a smooth base. They also introduced the Poincare residue formula in this case, which takes care the action of $G$, so that one can define the period integrals similarly as in toric cases. In this talk, I shall explain these techniques and show that the period integrals satisfy the tautological system.