Christopher Hacon
Deformations of canonical pairs
Abstract: It is known that results concerning the extension of
pluricanonical forms from a divisor to the ambient variety (such as
Siu's celebrated theorem on the deformation invariance of plurigenera)
have important consequences on the deformations of singularities of
algebraic varieties. For example, by work of Kawamata and Nakayama, it
is known that deformations of canonical/terminal singularities are
also canonical/terminal.
In this talk we will discuss the problem of
deformation invariance for canonical/klt log pairs (X,D) and for the
sections of the corresponding pluricanonical ring. Using these
results we will also study deformations of Fano varieties with
terminal singularities.
This is joint work with T. de Fernex.