Abstract
Using a filtration on the Grothendieck ring of triangulated categories, we define the motivic categorical dimension of a birational map between smooth projective varieties. We show that birational transformations of bounded motivic categorical dimension form subgroups, which provide a nontrivial filtration of the Cremona group. We discuss some geometrical aspect and some explicit example. We can moreover define, in some cases, the genus of a birational transformation, and compare it to the one defined by Frumkin in the case of threefolds.
Citation
Marcello BERNARDARA. "Categorical dimension of birational transformations and filtrations of Cremona groups." J. Math. Soc. Japan 73 (3) 861 - 883, July, 2021. https://doi.org/10.2969/jmsj/82658265
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