Categorical dimension of birational transformations and filtrations of Cremona groups
- 27 July 2021
- journal article
- research article
- Published by Mathematical Society of Japan (Project Euclid) in Journal of the Mathematical Society of Japan
- Vol. 73 (3), 1-23
- https://doi.org/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.Keywords
Other Versions
This publication has 8 references indexed in Scilit:
- Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fieldsProceedings of the London Mathematical Society, 2018
- Derived Categories View on Rationality ProblemsLecture Notes in Mathematics, 2016
- Hodge theory and derived categories of cubic fourfoldsDuke Mathematical Journal, 2014
- On the Jordan–Hölder property for geometric derived categoriesAdvances in Mathematics, 2014
- Derived categories and rationality of conic bundlesCompositio Mathematica, 2013
- Base change for semiorthogonal decompositionsCompositio Mathematica, 2011
- The universal Euler characteristic for varieties of characteristic zeroCompositio Mathematica, 2004
- Dynamic triggering of earthquakes: The nonlinear slip‐dependent friction caseJournal of Geophysical Research, 2002