GTM seminar

Speaker: Hsueh-Yung Lin (Kavli IPMU)
Title: Motivic invariants of birational maps and Cremona groups
Date (JST): Thu, Jun 10, 2021, 15:30 - 17:00
Place: Zoom
Abstract: (Joint with E. Shinder and S. Zimmerman) In characteristic zero, birational maps of projective varieties factorize through a sequence of blow-ups and blow-downs along smooth centers. In this talk, we will study to which extent these factorization centers are unique. We construct motivic invariants of birational maps which account for the non-uniqueness of centers. For surfaces over a perfect field, we prove the uniqueness of centers in the strongest possible sense. In higher dimension, the centers fail to be unique and the non-uniqueness has applications on Cremona groups, which eventually leads to negative answers to questions of Cheltsov and Dolgachev.