VIRTUAL WORKSHOP
Varieties with Trivial Canonical Class (event 2250)
Variétés de la classe canonique triviale
Dates: 06-10 April 2020 & 13-17 April 2020
Jorge Vitorio Pereira(IMPA & Aix-Marseille Université) 
​Introductory interview to the workshop 
Due to the Covid-19 epidemics, this workshop could not take place in residence at CIRM as originally intended.
SCIENTIFIC COMMITTEE
DESCRIPTION
The workshop aims at reviewing the recent decomposition theorem for singular varieties with trivial canonical class. The decomposition theorem is the culmination of the efforts of several mathematicians, and the workshop Varieties with Trivial Canonical Class brings together many of the researchers who contributed to the proof of it. We will also have some talks on the geometry of hyperkähler varieties. ​
ORGANIZING COMMITTEE
SPEAKERS
TALKS & DISCUSSION
The talk by Ekaterina Amerik is independent of the other talks. The talk 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. Suggested below is one possible natural order to watch the nine lectures that discuss the decomposition theorem.
1. The decomposition theorem: the smooth case
Arnaud Beauville - Université Côte d'Azur
2. Structure theory for singular varieties with trivial canonical divisor
​Daniel Greb - University of Duisburg-Essen
3. A decomposition theorem for singular spaces with trivial canonical class
​(part 1) 
​Henri Guenancia - CNRS, Université Paul-Sabatier
​(2019 talk filmed by Institut Fourier, Grenoble)
4. A decomposition theorem for singular spaces with trivial canonical class
​(part 2)
Henri Guenancia - CNRS, Université Paul-Sabatier
​(2019 talk filmed by Institut Fourier, Grenoble)
5. Kit varieties with trivial canonical class: Holonomy, differential forms and fundamental groups II - Analytical aspects -
Henri Guenancia - CNRS, Université Paul-Sabatier
6. A decomposition theorem for singular spaces with trivial canonical class
​(part 3)
Andreas Höring - Université Nice Sophia Antipolis
​​(2019 talk filmed by Institut Fourier, Grenoble)
7. A decomposition theorem for singular spaces with trivial canonical class
(part 4)
Stéphane Druel - CNRS, Université Lyon 1 
​​(2019 talk filmed by Institut Fourier, Grenoble)
8. A decomposition theorem for singular spaces with trivial canonical class
(part 5)
Stéphane Druel - CNRS, Université Lyon 1 
​​(2019 talk filmed by Institut Fourier, Grenoble)
9. A splitting theorem
​Stéphane Druel - CNRS - Université Lyon 1 
Rational curves and contraction loci on holomorphic symplectic manifolds
Ekaterina Amerik - Université Paris-Saclay
Virtual discussion session
Speakers of the workshop gather together online to discuss how the proof of the decomposition theorem came to be. 
​Virtual problem session
Presentation of open problems on the subject, intertwined with comments by the speakers of the workshop. 
REFERENCES
 
Arnaud Beauville. 
Variétés Kähleriennes dont la première classe de Chern est nulle.
J. Differential Geom. 18 (1983), no. 4, 755–782 (1984).
Mathscinet     zbMATH          Journal
 
Daniel Greb; Stefan Kebekus; Thomas Peternell. 
Singular spaces with trivial canonical class.
Minimal models and extremal rays (Kyoto, 2011), 67–113, Adv. Stud. Pure Math., 70, Math. Soc. Japan, [Tokyo], 2016.
Mathscinet     zbMATH          Journal            arXiv
 
Jorge Vitório Pereira; Frédéric Touzet. 
Foliations with vanishing Chern classes.
Bull. Braz. Math. Soc. (N.S.) 44 (2013), no. 4, 731–754.
Mathscinet     zbMATH          Journal            arXiv
 
Stéphane Druel. 
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five.
Invent. Math. 211 (2018), no. 1, 245–296.
Mathscinet     zbMATH          Journal            arXiv
 
Stéphane Druel; Henri Guenancia.
A decomposition theorem for smoothable varieties with trivial canonical class. 
J. Éc. polytech. Math. 5 (2018), 117–147.
Mathscinet     zbMATH          Journal            arXiv

Henri Guenancia.
Semistability of the tangent sheaf of singular varieties.
​Algebr. Geom. 3 (2016), no. 5, 508–542.
Mathscinet     zbMATH         Journal           arXiv

Daniel Greb; Henri Guenancia; Stefan Kebekus. 
Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups.
Geom. Topol. 23 (2019), no. 4, 2051–2124.
Mathscinet    zbMATH          Journal            arXiv
 
Andreas Höring; Thomas Peternell. 
Algebraic integrability of foliations with numerically trivial canonical bundle. 
​Invent. Math. 216 (2019), no. 2, 395–419.
Mathscinet    zbMATH          Journal            arXiv