Tsinghua University Shiing-Shen Chern Distinguished Lecture
Student No.:100
Time:16:30-17:30, 2017.10.18/ 10.20/ 10.23/ 10.25
Instructor:Claire Voisin  
Place:Lecture Hall, Floor 3, Jinchun Yuan West Building
Starting Date:2017-10-18
Ending Date:2017-10-25

Lecture 1  Introductory lecture on Kähler and Calabi-Yau geometry

I will describe the  complex differential geometric viewpoint on Calabi-Yau geometry, and some consequences.


Lecture 2  Hodge theory: applications to  deformation  theory and topology

Hyper-Kähler manifolds are easy to deform and their deformations are almost entirely controled by their period points (work of Beauville, Huybrechts and Verbitsky). I will also explain how the existence of the Beauville-Bogomolov form follows from the local study of the period map.


Lecture 3  Constructing hyper-Kähler manifolds from algebraic geometry


The simplest hyper-Kähler manifolds are K3 surfaces and there are many other types that have been constructed starting from K3 surfaces. More surprisingly, cubic fourfolds also led to the construction of several families, with the advantage over K3 that they have 20 parameters, while algebraic K3 surfaces have only 19 parameters.



Lecture 4  Deformation types of hyper-Kähler manifolds via degeneration.

I will explain a simple but useful generalization of Huybrechts' theorem on birational versus deformation equivalence, and  apply it to several classes of examples.