Hyperkahler varieties are one of the basic building blocks of algebraic varieties, but the known methods for constructing them are scarce. The goal of this school is to explain a new method, based on moduli spaces of objects in K3 categories, that unifies the main previously known constructions. The lecture series will focus on the two general theories needed for this purpose: stability conditions and semiorthogonal decompositions. The main prerequisite is basic knowledge of algebraic geometry; familiarity with derived categories would also be very useful, but the key points of this theory will be quickly reviewed in one of the lectures.
Emanuele Macrí, Stability conditions and hyperkähler moduli spaces
Alex Perry, Semiorthogonal decompositions and K3 categories (notes)
Program of the school: Two lectures each day via Zoom (approximately 60 minutes each). Problem sessions for all the participants are not planned, but we encourage you to organize local working groups to solve problems accompanying the lectures.
The school is aimed (mainly, but not only) at graduate students and young researchers in algebraic geometry and related areas.
Schedule, except for Tuesday, September 14:
2 pm (CET): Emanuele Macrí, Stability conditions and hyperkähler moduli spaces
3:45 pm (CET): Alex Perry, Semiorthogonal decompositions and K3 categories
Schedule for Tuesday, September 14:
1 pm (CET): Emanuele Macrí, Stability conditions and hyperkähler moduli spaces
3:45 pm (CET): Alex Perry, Semiorthogonal decompositions and K3 categories
Possibility of chatting with other participants, in real life known as coffee breaks, via Gather: here is our space, the password will be given during the lectures.
Organizers: Maria Donten-Bury (University of Warsaw), Grzegorz Kapustka (Jagiellonian University in Kraków) and Michał Kapustka (Polish Academy of Sciences).
Help with organizing local working groups: Maciej Gałązka in Warsaw and Kacper Grzelakowski in Cracow.
Registration: Please register by sending an email to Maria Donten-Bury,
marysia [at] mimuw [dot] edu [dot] pl before August 31, 2021. Please give your affiliation and, if you are a student, the name of your supervisor.
The links to Zoom meetings will be sent to registered participants.
All inquiries should be directed to Maria Donten-Bury, marysia [at] mimuw [dot] edu [dot] pl.
The school is organized in the framework of several research projects: NCN Sonata Bis 2017/26/E/ST1/00231 of Jarosław Buczyński Complex contact manifolds and geometry of secants, NCN Sonata 2017/26/D/ST1/00755 of Maria Donten-Bury Algebraic varieties related to combinatorial structures, NCN Sonata Bis 2018/30/E/ST1/00530 of Grzegorz Kapustka Rozmaitości hyperkaehlerowskie, NCN Opus 2018/31/B/ST1/02857 of Michał Kapustka Rozmaitości typu Calabi-Yau.