Factorization Centers in Dimension Two and the Grothendieck Ring of Varieties

Speaker: Evgeny Shinder
Affiliation: University of Sheffield
10/07/20

I explain the concept of factorization centers for birational isomorphisms. The main result is that for smooth projective surfaces over perfect fields these factorization centers for a birational isomorphism f: X- Y are independent of the choice of f and only depend on X and Y. The proof relies on the two dimensional MMP providing the minimal models for surfaces and the link decomposition for morphisms. I explain the relationship to the rationality problem for surfaces and to the structure of the Grothendieck ring of varieties. This is joint work with H.-Y. Lin and S. Zimmermann.