Wenhan Dai

3264 and All That

Seminar on Enumerative Geometry.

The number in the title of this book is a reference to the solution of a classic problem in enumerative geometry: the determination, by Chasles, of the number of smooth conic plane curves tangent to five given general conics. The problem is emblematic of the dual nature of the subject.

• Time: Every Monday, 15:00-17:00pm.
• Location: Quan Zhai #9, Jingchun Yuan.
• Instructor: Zhiyu Tian.

Main reference

• [EH16] D. Eisenbud and J. Harris, 3264 and All That. Cambridge University Press. 2016. (download)

Syllabus

• (9/27) Zhiyu Tian: Introduction and organization.
• (No meeting during the national day’s holiday.)
• (10/11) Xiaozheng Han: The G(1,3).
• (10/18) Chongyu Wang: Grassmannian.
• (10/25) Xinpeng Jiang: Chern classes.
• (11/1) Hanfei Guo: Lines on hypersurfaces.
• (11/8) Jiyao Tang: Singular elements of linear series.
• (11/15) Xiangtao Chen: Compactification.
• (11/22) Yang Liu: Projective bundle and their Chow groups.
• (11/29) Xingzhu Fang: Segre class and the variety of linear spaces.
• (12/6) Yang Liu: The contact problems.
• (12/13) Shuting Shen: The Porteous problem.
• (12/20) Wenhan Dai: Excess intersections and blow-ups.
• (12/27) Yu Tian: Grothendieck-Riemann-Roch theorem.

Here are my notes for the second last talk.

Generic transversality to a cycle: