Hsueh-Yung Lin, Motivic Invariants of Birational Automorphisms of Threefolds

The motivic invariant c(f) of a birational automorphism f : X – → X measures the difference between the birational types of the exceptional divisors of f and those of the inverse f^-1. In general c(f) is nonzero: this is the case when f is some Cremona transformation, which leads to new explanation as to why Cremona groups are not simple. In the other direction, which will be the main focus of the talk, we show that the invariant c(f) always vanishes when X is a complex projective threefold. (joint work in progress with E. Shinder.)