Codes MSC :
37F75 - Holomorphic foliations and vector fields

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. 

The virtual workshop consist of ten talks and two online sessions. Five of the talks 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. we have host 2 online sessions with the speakers of the conference with the possibility of online intervention by the registered participants of the workshop.

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

Voir aussi

• [Virtualconference] Varieties with Trivial Canonical Class: problem session / Animateur Pereira, Jorge Vitório. CIRM
  
• [Virtualconference] Varieties with Trivial Canonical Class: discussion session / Animateur Pereira, Jorge Vitório. CIRM
  
• [Virtualconference] Interview at CIRM: Jorge Vitório Pereira / Personne interviewée Pereira, Jorge Vitório ; Intervieweur Vareilles, Stéphanie. CIRM
  
• [Virtualconference] The decomposition theorem: the smooth case / Auteur de la Conférence Beauville, Arnaud. CIRM
  
• [Virtualconference] Holonomy of singular Ricci-flat metrics / Auteur de la Conférence Guenancia, Henri. CIRM
  
• [Virtualconference] Structure theory for singular varieties with trivial canonical divisor / Auteur de la Conférence Greb, Daniel. CIRM
  
• [Virtualconference] Rational curves and contraction loci on symplectic manifolds / Auteur de la Conférence Amerik, Ekaterina. CIRM
  

Arnaud Beauville. Variétés Kähleriennes dont la première classe de Chern est nulle. J. Differential Geom. 18 (1983), no. 4, 755–782 (1984). - http://dx.doi.org/10.4310/jdg/1214438181


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. - http://dx.doi.org/10.2969/aspm/07010067


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. - https://doi.org/10.1007/s00222-017-0748-y


Stéphane Druel; Henri Guenancia. A decomposition theorem for smoothable varieties with trivial canonical class. J. Éc. polytech. Math. 5 (2018), 117–147. - https://doi.org/10.5802/jep.65


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. - https://doi.org/10.2140/gt.2019.23.2051


Andreas Höring; Thomas Peternell. Algebraic integrability of foliations with numerically trivial canonical bundle. Invent. Math. 216 (2019), no. 2, 395–419. - https://doi.org/10.1007/s00222-018-00853-2


PEREIRA, Jorge Vitório et TOUZET, Frédéric. Foliations with vanishing Chern classes. Bulletin of the Brazilian Mathematical Society, New Series, 2013, vol. 44, no 4, p. 731-754 - https://doi.org/10.1007/s00574-013-0032-8


GUENANCIA, Henri, Semistability of the tangent sheaf of singular varieties. Algebr. Geom. 3 (2016), no. 5, 508–542. - https://doi.org/10.14231/AG-2016-024