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

## May 13 @ 2:30 pm - 3:30 pm KST

B236-1,
IBS
Korea, Republic of

*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.)