Some characterizations of compact flat Kaehler  manifolds/orbifolds (quotients of compact complex tori)


Shin-Yi Lu

14:00:00 - 16:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

This consists of two separate parts.
First part: (key player is the Ricci Curvature) I will go over Yau's differential geometric solution  to the problem via the first two Chern classes and  state (with some motivation) our very recent characterizations of the object stated in the title  amongst some mildly singular varieties.
  Second part: (key player here is the holomorphic  sectional curvature) With some preparation, I will give a proof of another characterization of such object in the class of compact Kaehler manifolds  with semi-negative holomorphic sectional curvature  via the vanishing of the total scalar curvature. This will lead to a structure theory for objects in this class that we will motivate and state.