課程名稱 
代數幾何專題 Topics in Algebraic Geometry 
開課學期 
1001 
授課對象 
理學院 數學研究所 
授課教師 
連文豪 
課號 
MATH5147 
課程識別碼 
221 U5360 
班次 

學分 
3 
全/半年 
半年 
必/選修 
選修 
上課時間 
星期三2,3,4(9:10~12:10) 
上課地點 
新數101 
備註 
總人數上限：30人 


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課程概述 
Given a family of projective manifolds, Hodge theory provides a way to study the variation of complex structures of the family of manifolds. Using the flat structure associated to their homology groups, one can construct certain locally defined period integrals, as a means to parametrize the complex structures. These integrals, however, depend on a number of choices in general which render them difficult to compute.
Thanks to Mirror Symmetry, a large class of distinguished families of projective manifolds  known as CalabiYau manifolds  have been found in recent years, where the period integrals can be constructed in a canonical fashion. In this topic course, this construction will be explained and given a new interpretation, which leads us to a vast generalization. In examples, we will give an explicit construction for a new class of partial differential equation systems that govern those period integrals.

課程目標 
The course is expository in nature, and as such all necessarily background will be reviewed, at least briefly. But the aim is to get to the latest development on the proposed topic. Open problems will also be discussed. The content is based on joint work with R. Song and S.T. Yau. 
課程要求 
Basics in complex differential geometry and algebraic geometry. 
預期每週課後學習時數 

Office Hours 

指定閱讀 
Bong H Lian, Ruifang Song and ShingTung Yau; Periods integrals and tautological systems, arXiv:1105.2984 
參考書目 
Bong H Lian, Ruifang Song and ShingTung Yau; Periods integrals and tautological systems, arXiv:1105.2984 
評量方式 (僅供參考) 
No. 
項目 
百分比 
說明 
1. 
Homework 
100% 


