On the Kodaira dimension of base spaces of projective families of manifolds


Behrouz Taji


University of Sydney


Tue, 17/09/2019 - 12:00pm to 1:00pm


RC-4082, The Red Centre, UNSW


A celebrated conjecture in algebraic geometry, which goes back to Shafarevich, predicts that variation in many  families of projective complex manifolds can be in some sense measured by the canonical birational invariant of their base spaces; the so-called Kodaira dimension. For example, a smooth family of curves of genus at least equal to 2 over the projective line (whose Kodaira dimension is zero) should be isotrivial (zero variation). My aim in this talk is to discuss this conjecture and its solution based on the combined works of Viehweg-Zuo, Popa-Schnell, Campana-Paun and myself. If time permits, I will also discuss a generalization of this problem.

School Seminar Series: