Seminar on Moduli of Sheaves, Fall 2017

This is the webpage of the student learning seminar on algebraic geometry at Columbia. The predecessor of this seminar is the Remynar, from which the template for this page is partially copied.

The goal of this seminar is to understand various aspects of moduli spaces of semistable sheaves on smooth projective varieties. In the first half of the semester, we will introduce the necessary ingredients and discuss the construction and general properties of these moduli spaces. We will then specialize to the case of K3 surfaces and study their Fourier-Mukai transformations. Other further topics are to be determined, depending on the interests of the participants.

References:

Please e-mail the organizers if you'd like to receive notifications.

Organizers: Raymond Cheng, Carl Lian.

Time and location: Tuesday 16:30-18:00 in Math 507 *except 26 September, 17:30 in Math 622

Date Speaker Title Ref.
5 Sep Organizational Meeting
12 Sep Carl Lian Stability; Harder-Narasimhan Filtration [HL] 1.2-1.5
19 Sep Raymond Cheng Quot Scheme; Relative Harder-Narasimhan Filtration [HL] 2
26 Sep* Monica Marinescu Boundedness on curves; Grauert-Mülich Theorem [HL] 1.7, 3.1
3 Oct Carl Lian Boundedness in general; Tensor Products of Semistable Sheaves [HL] 3.2-3.3
10 Oct Noah Arbesfeld Geometric Invariant Theory [HL] 4.2
17 Oct Construction of Moduli Space, I [HL] 4.3-4.4
24 Oct Construction of Moduli Space, II; Local Structure [HL] 4.4-4.6
31 Oct Henry Liu Moduli of Sheaves on K3 Surfaces [HL] 6.1
7 Nov No talk: university holiday
14 Nov Shuai Wang Fourier-Mukai Transforms on K3 Surfaces [H] 10
21 Nov
28 Nov
5 Dec Qixiao Ma Reconstruction [BO]
12 Dec