Derived invariance of the Albanese relative canonical ring

Abstract

We show the derived invariance of various geometric invariants of smooth complex projective varieties governed by the Albanese map, including the relative canonical ring and the class of the relative canonical model in a suitable variant of the Grothendieck ring of varieties. Then we derive some applications to the derived invariance of Hodge numbers.

arXiv comment37 pages. Final version. To appear on Advances in Mathematics