Giancarlo Urzúa _ Pontificia Universidad Católica de Chile
Categorical aspects of the Kollár--Shepherd-Barron correspondence
1. W-surfaces and their birational geometry
2. N-resolutions and the Kollár--Shepherd-Barron correspondence
3. S.o.d.'s from N-resolutions: results and open problems
Kyoung-Seog Lee _ University of Miami
Derived categories and VGIT
Giancarlo Urzúa
Categorical aspects of the Kollár--Shepherd-Barron correspondence
1. W-surfaces and their birational geometry
Brief introduction to W-surfaces and their properties. Examples from degenerations of the projective plane and Enriques surfaces. The MMP machinery (including flips and divisorial contractions) and their outcomes, Mori trains.
2. N-resolutions and the Kollár--Shepherd-Barron correspondence
Irreducible components of the deformation space of a cyclic quotient singularity and the correspondences, which introduce N-resolutions. General set-up with Wahl resolutions. Zero continued fractions and algorithm for M-resolutions. Existence and uniqueness of N-resolution via continued fractions. The example from a minimal resolution.
3. S.O.D.'s from N-resolutions: results and open problems
Another way to find the N-resolution of an M-resolution, and the braid group action. The set-up for the main theorems about Hacking exceptional collections. Some applications (e.g. to every simply-connected Dolgachev surface), and some open questions (e.g. admissible embeddings of derived categories of modules over quiver algebras into derived categories of surfaces).
Kyoung-Seog Lee
Derived categories and VGIT
In this talk, I will review the works of Halpern-Leistner and Ballard-Favero-Katzarkov, studying how derived categories change under the VGIT. Then I will discuss how one can use these works to study derived categories of certain interesting algebraic varieties. The last part of this talk is based on joint work with Han-Bom Moon.
10:30–11:20: Urzúa 1
11:30–12:20: K. Lee (via zoom: 313 252 8553)
14:00–14:50: Urzúa 2
15:00–15:50: Urzúa 3
Heesang Park _ Konkuk University
Dongsoo Shin _ Chungnam National University
Basic Research Laboratory: ASADCS
Research Institute of Basic Sciences, Konkuk University
Dongsoo Shin: dsshin@cnu.ac.kr