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.
Please e-mail the organizers if you'd like to receive notifications.
Time and location: Tuesday 16:30-18:00 in Math 507 *except 26 September, 17:30 in Math 622
|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|
|5 Dec||Qixiao Ma||Reconstruction||[BO]|