Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

Source abstract

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Păun, confirming a special case of Iitaka’s C n , m C_{n,m} conjecture: if f : X → Y f \colon X\to Y is an algebraic fiber space, and if the Albanese mapping of Y Y is generically finite over its image, then we have the inequality of Kodaira dimensions κ ( X ) ≥ κ ( Y ) + κ ( F ) \kappa (X)\geq \kappa (Y)+\kappa (F) , where F F denotes a general fiber of f f . We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Păun, and Takayama).