AAG Seminar: Luigi Lombardi (Stony Brook)

Title: A decomposition theorem for the pushforwards of pluricanonical bundles to abelian varieties

 

Abstract: In this talk I will describe a direct-sum decomposition in pull-backs of ample sheaves for the pushforwards of pluricanonical bundles via a morphism from a smooth projective variety to an abelian variety. The techniques for proving this decomposition rely on generic vanishing theory, and a recent result of Paun-Takayama on the existence of a semipositive singular hermitian metric on a pushforward of an adjoint bundle. Time permitting, I will provide an application of the above decomposition to the problem of understanding the global generation property of pluricanonical divisors on (possibly singular) varieties of general type. This is a joint work in progress with M. Popa and C. Schnell.