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July, 2021 Categorical dimension of birational transformations and filtrations of Cremona groups
Marcello BERNARDARA
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J. Math. Soc. Japan 73(3): 861-883 (July, 2021). DOI: 10.2969/jmsj/82658265

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.

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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

Information

Received: 14 May 2019; Revised: 14 February 2020; Published: July, 2021
First available in Project Euclid: 13 April 2021

Digital Object Identifier: 10.2969/jmsj/82658265

Subjects:
Primary: 14E07
Secondary: 14F05

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 3 • July, 2021
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