On the Albanese fibration for singular varieties with nef anticanonical divisor

Stefano Filipazzi (EPFL)

Wednesday 1st May 16:00-17:00 Maths 110


To every normal projective variety X one can associate an Abelian variety Alb(X), called the Albanese variety of X, and a morphism alb:X->Alb(X), called the Albanese morphism. In many situations, the geometry of X can be investigated through alb. In particular, if X has klt singularities (e.g., it is smooth) and -K_X is nef, then alb is a surjective analytically locally trivial fibration. In this talk, we investigate what happens if we relax the condition on the singularities of X. First, we show that alb need not be surjective if the singularities are arbitrary. Then, we show that alb is still surjective and flat if X has log canonical singularities. To conclude, we exhibit an example of log canonical log Calabi-Yau pair whose Albanese morphism is not isotrivial, not even birationally. Time permitting, we will discuss implications of this example for the Beauville-Bogomolov decomposition of log canonical pairs. This talk is based on current work in progress with F. Bernasconi, Zs. Patakfalvi, and N. Tsakanikas.

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