MORLET SEMESTER 1 – Virtual Workshop – Varieties with Trivial Canonical Class

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Date/heure
Date(s) - 13/04/2020 - 17/04/2020
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Emplacement
CIRM, Luminy

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Interview at CIRM: Jorge Vitório Pereira
Jean Morlet Chair Holder – 2020/Semester 1
Varieties with Trivial Canonical Class
​​
April 13 to 17

​JEAN-MORLET CHAIR – WORKSHOP

Frank Loray (CNRS – Université de Rennes I)
Jorge Vitório Pereira (IMPA Brazil / Aix-Marseille Université)
Erwan Rousseau (Aix-Marseille Université)

The workshop aims at reviewing the recent decomposition theorem for singular varieties with trivial canonical class. This result is the culmination of efforts of a number of researchers and this workshop brings together most researchers which contributed to the proof of this result. We will also have some talks on the geometry of hyperkähler varieties. 

Due to the unusual circumstances, we have to experiment with a different format. The virtual workshop will consist of ten talks and two online sessions. Five of the talks figuring here are original from the Summer School on Foliations and Algebraic Geometry, which took place at Institut Fourier, Grenoble in from June-July  2019. The other five talks were recorded specially for the virtual workshop. On Tuesday, April 14, and on Thursday, April 16, we will host online sessions with the speakers of the conference with the possibility of online intervention by the registered participants of the workshop.

SPEAKERS

Ekaterina Amerik (Université Paris-Sud)
Arnaud Beauville (Université Nice Sophia-Antipolis)
Stéphane Druel (CNRS, Université Lyon 1)
Daniel Greb (University of Duisburg-Essen)
Henri Guenancia (CNRS, Université Toulouse Paul-Sabatier)
Andreas Höring (Université Nice Sophia Antipolis)

VIRTUAL DISCUSSIONS SCHEDULE
  • TUESDAY 14 APRIL


​Discussion session

Speakers of the workshop will gather together online to discuss how the proof of the decomposition theorem came to be. 

  • THURSDAY 16 APRIL

3pm : Problem session

Presentation of open problems on the subject, intertwined with comments by the speakers of the workshop.  ​​

Suggested order for watching the lectures

The talk “Rational Curves and Contraction Loci on Holomorphic Symplectic Manifolds” by Ekaterina Amerik is independent of the other talks. The talk “The Decomposition Theorem: the Smooth Case” by Arnaud Beauville reviews the history of the decomposition theorem for smooth varieties and sketches its proof. All the other eight talks are about the decomposition theorem for varieties with singular canonical class. Below, one possible natural order to watch the nine lectures that discuss the decomposition theorem.1. Beauville. The decomposition theorem: the smooth case
2. Greb. Structure theory for singular varieties with trivial canonical divisor
3. Guenancia. A decomposition theorem for singular spaces with trivial canonical class (part 1)
4. Guenancia.  A decomposition theorem for singular spaces with trivial canonical class (part 2)
5. Guenancia. Holonomy of singular Ricci-flat metrics
6. Höring. A decomposition theorem for singular spaces with trivial canonical class (part 3)
7. Druel. A decomposition theorem for singular spaces with trivial canonical class (part 4)
8. Druel. A decomposition theorem for singular spaces with trivial canonical class (part 5)
9.  Druel. A splitting theorem


RECORDED TALKS – CIRM VIRTUAL CONFERENCES & INSTITUT FOURIER VIDEOS – TOPICS OF DISCUSSIONS 
The decomposition theorem: the smooth case
​By Arnaud Beauville – Université Côte d’Azur
A decomposition theorem for singular spaces with trivial canonical class (part 1)
By Henri Guenancia – CNRS, Université Paul-Sabatier
Holonomy of singular Ricci-flat metrics

By Henri Guenancia – CNRS, Université Paul-Sabatier
A decomposition theorem for singular spaces with trivial canonical class (part 4)
By Stéphane Druel – CNRS – Université Claude Bernard Lyon 1
A splitting theorem

By Stéphane Druel – CNRS – Université Claude Bernard Lyon 1
Structure theory for singular varieties with trivial canonical divisor
By Daniel Greb – University of Duisburg-Essen
A decomposition theorem for singular spaces with trivial canonical class (part 2)
By Henri Guenancia – CNRS, Université Paul-Sabatier
A decomposition theorem for singular spaces with trivial canonical class (part 3)
By Andreas Höring
A decomposition theorem for singular spaces with trivial canonical class (part 5)
By Stéphane Druel – CNRS – Université Claude Bernard Lyon 1 ​
Rational curves and contraction loci on holomorphic symplectic manifolds
By Ekaterina Amerik – Université de Paris-Sud


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