Geometry and Complex Analysis Seminar
Student No.:20
Time:Tue, 15:20-16:55, Oct.9-Jan.15
Instructor:Tian Yin, Wu Yunhui, Xiao Jian  
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-10-9
Ending Date:2019-1-15


Speaker: Jie LIU (Morningside Center of Mathematics, CAS)

Title: Anticanonical geometry of Fano manifolds with coindex four

Abstract: Fano manifolds are fundamental objects studied in complex geometry and algebraic geometry, and it is well-known that all Fano manifolds of given dimension form a bounded family. Thus it is natural to ask if it is possible to classify them. This was already done for Fano manifolds of coindex at most three. However, up to now the classification of Fano manifolds with coindex four is very far from known even in dimension four. In this talk, I will present our recent results on the geometry of the pluri-anticanonical systems of Fano manifolds with coindex four. In particular, I will explain its relation with polarized (singular) Calabi-Yau threefolds. If time is permitted, open questions and difficulties will also be discussed.


Speaker: Jian XIAO (Tsinghua University)

Title: Group discussions -- some problems in complex algebraic geometry


Speaker: Baohua FU (Chinese Academy of Sciences)

Title: On Fano complete intersections in rational homogeneous varieties

Abstract: Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if X=\cap_{i=1}^r D_i \subset G/P a general complete intersection of r ample divisors such that K^*_{G/P} \otimes O_{G/P}(-\sum_i D_i) is ample, then X is Fano. We first classify these Fano complete intersections which are locally rigid. It turns out that most of them are hyperplane sections. We then classify general hyperplane sections which are quasi-homogeneous.