Chen-Jiang decompositions for projective varieties, without Hodge modules

TL;DR

This paper provides a new proof that the direct image of the canonical bundle of a smooth projective variety admits a Chen-Jiang decomposition, avoiding the use of Hodge modules, thus simplifying the understanding of this geometric property.

Contribution

It introduces a novel proof technique for Chen-Jiang decompositions that does not rely on Hodge module theory, expanding the toolkit for algebraic geometers.

Findings

Direct image of canonical bundle admits Chen-Jiang decomposition

Proof avoids Hodge module theory

Simplifies understanding of decomposition properties

Abstract

We give a new proof of a theorem by Pareschi, Popa and Schnell that the direct image of the canonical bundle of a smooth projective variety along a morphism to an abelian variety admits a Chen-Jiang decomposition, without using the theory of Hodge modules.