Compact K\"ahler threefold with nef anticanonical line bundle

Abstract: In my talk, I will discuss a recent collaboration with Shin-ichi Matsumura on compact Kähler threefolds with nef anticanonical line bundles. Thanks to the breakthrough result of Cao-Höring, we can focus on the non-projective case. Using the Kähler threefold MMP developed by Höring-Peternell, we have shown that there are only three possibilities for such manifolds: (1) Calabi-Yau manifolds; (2) projectivizations of numerical flat vector bundles over a torus; (3) products of K3 surfaces with projective lines. I will begin by reviewing the arguments of Cao-Höring and then explain the different ingredients we used to establish our results in the Kähler setting.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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