Derived invariance of the Albanese relative canonical ring

TL;DR

This paper proves that certain geometric invariants related to the Albanese map, such as the relative canonical ring, are preserved under derived equivalences, with applications to Hodge number invariance.

Contribution

It establishes the derived invariance of the relative canonical ring and related invariants for smooth complex projective varieties, extending understanding of derived equivalences.

Findings

Derived invariance of the relative canonical ring

Invariance of the class of the relative canonical model in the Grothendieck ring

Applications to the invariance of Hodge numbers

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.