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K3 surfaces and
their Picard lattice
Graduate course in Rijksuniversiteit Groningen
Dino Festi
Description: This course is aimed to PhD students, but suitable also for advanced Master students and young researchers, and its goal is to give an overview on the theory of K3 surfaces and their Picard lattice.
We want to illustrate how to compute the Picard number or the Picard lattice of a given K3 surface,
and how to count the elliptic fibrations of a K3 surface with a given Picard lattice.
The lectures will be online, on tuesdays, 11:00--13:00. The course will start on Tuesday 26 October and will consists of 8 lectures.
The credential to access the meeting will be communicated short in advance via email to the registered participants.
If you want to participate, please contact Dino Festi or Pınar Kılıcer.
Plan of the course and references.
Prerequisites: some algebraic geometry over the complex and finite fields (definition of a variety, definition of a scheme, divisors, linear systems), basics of sheaf cohomology, basics of group theory.
Schedule
26/10: Introduction to K3 surfaces and their Picard lattice. Notes.
02/11: Overview on lattices. Notes.
09/11: No lecture
16/11: Global Torelli theorem and the Period map. Notes.
23/11: The Picard lattice of K3 surfaces under specialization. Notes.
30/11: Van Luijk's method to bound the Picard number. Notes.
07/12: An explicit example. Notes. Magma code.
14/12: A practical method to compute the (geometric) Picard lattice of a K3 surface of degree two.
Notes (TeX). Notes.21/12: Application to singular models of K3 surfaces. Notes.
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