Trivial Canonical Class Discussion Session April 14, 2020 - PowerPoint PPT Presentation

Varieties with Trivial Canonical Class Discussion Session April 14, 2020

Presentation • 10 lectures available on YouTube • 5 lectures recorded last week • 5 lectures were recorded during the Summer School Foliations and Algebraic Geometry hosted at the Institut Fourier, Grenoble back in 2019. • Information about the workshop, including references and links to the talks, can be found at the website https://www.cirm-math.com/virtual-event-2250.html

Lectures

Lectures Ekaterina Amerik

Lectures Arnaud Beauville

Lectures Daniel Greb

Lectures Henri Guenancia

Lectures Andreas Höring

Lectures Stéphane Druel

Why study (s (singular) varieties with trivial canonical class ? ? According to the current More precisely, singular philosophy in birational geometry, varieties with trivial canonical class varieties with trivial canonical class and klt singularities, conjecturally, are one of the building blocks of appear as general fibers of the Iitaka- arbitrary algebraic varieties, Kodaira fibration of the minimal model together with Fano varieties and of non-uniruled varieties. varieties of general types.

Decomposition Theorem for Singular Varieties Statement

Decomposition Theorem for Singular Varieties Timeline October, 2011 - Singular spaces with trivial canonical class by Greb, Kebekus, and Peternell. June, 2016 - A decomposition theorem for singular spaces with trivial canonical class of dimension at most five by Druel April, 2017 - Klt varieties with trivial canonical class – Holonomy, differential forms, and fundamental groups by Greb, Guenancia, and Kebekus October, 2017 - Algebraic integrability of foliations with numerically trivial canonical bundle by Höring and Peternell Dates are from the original arXiv submission.

Questions