Topics in K3 surfaces and derived categories

Time: Thursday 3:30pm-4:30pm (Berkeley time)
Room: 730 Evans Hall (UC Berkeley)
Zoom: This is a hybrid-style seminar. Reach out to the organizer for a Zoom link.
Organizer: Daigo Ito (Please email the organizer if you are interested.)

Schedule

12/13/2023 Daigo Ito Rough overview of topics in K3 surfaces ([K3, 7,10,13,16], [FM, 10]) Note
12/22/2023 Garrett Brown Defintions and basic properties of K3 surfaces [K3, 1.1-1.3] Note
12/29/2023 Daigo Ito Mukai vectors/pairings and Grothendieck-Riemann-Roch theorem ([K3, 9.1], [FM, 5.2]) Note
1/5/2024 Daigo Ito Algebraic approach to slope stabiliy of tangent bundle ([K3, 9.2,9.4]) Note
1/23/2024 Daigo Ito Algebraic approach to slope stabiliy of tangent bundle (cont'd) ([K3, 9.2,9.4]) Note
1/30/2024 Daigo Ito Moduli of vector bundles and Gieseker stability ([K3, 10.1.1, 10.1.3]) Note
2/6/2024 Daigo Ito Gieseker stability on a surface and the Jordan–Hölder filtration ([K3, 10.1.3, 10.1.4]) Note
2/13/2024 Feiyang Lin Moduli problem of semi-stable sheaves ([K3, 10.1.2, 10.1.5], [HL, 4.1, 4.2]) Note
2/20/2024 Feiyang Lin GIT quoteints and construction of moduli of semi-stable sheaves ([K3, 10.1.5]) Note
2/29/2024 Ruoxi Li Local structure of moduli of semi-stable sheaves ([K3, 10.1.6]) Note

Reference

[K3] Daniel Huybrechts, Lectures on K3 surfaces
[FM] Daniel Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry
[HL] Daniel Huybrechts and Manfred Lehn, The Geometry of Moduli Spaces of Sheaves