Conférence GAGC 2016 (en 2017)

The eventual paracanonical map of an irregular variety.

Non programmé

50m

CIRM, Luminy

Orateur

Rita Pardini

Description

I will report on joint work with. M.A. Barja (UPC, Barcelona) and L. Stoppino (Universita' dell'Insubria, Italy) Given a map $a:X⟶A$ from a smooth projective variety to an abelian variety and a line bundle $L$ on $X$, we study the "eventual" behaviour of the linear system $|L|$ under base change with the $d$-th multiplication map $A⟶A$. We prove a factorization theorem stating, roughly speaking, that the correponding map stabilizes for $d$ large and divisible enough. When $X$ is of general type, $A$ is the Albanese map and $L$ is the canonical bundle, we obtain the so-called "eventual paracanonical" map, which is a new geometrical object intrinsically attached to $X$. REFERENCES: arXiv: 1606.03301, arXiv: 1606.03290