An update of the completion problem on Calabi-Yau moduli spaces


Shi-Ming Chen  ( National Taiwan University )
2016-11-02  15:30 - 16:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

I will survey recent advances on the correspondences between (1) finite Weil-Petersson distance degenerations of CY manifolds, (2) degenerations of CY manifolds with canonical singularities, and (3) degenerations of CY with bounded diameters. For one parameter moduli the equivalence of (1) and (2) had been solved with the help of semi-stable minimal model program of CY manifolds developed by Fujino and Lai. The further equivalence with (3) had been carried out recently by Takayama and Tosatti based on the theory of Hausdorff convergence developed by Donaldson-Sun and Rong-Zhang. For moduli with more than one dimensions I will discuss the possible approach on it based on the conjectural monodromy criterion of finite WP distance degenerations. References: C.-L. Wang: Aspects on Calabi-Yau moduli. Available at