Polarizable twistor D-modules

TL;DR

This paper introduces polarized twistor D-modules and proves a Decomposition Theorem for their direct images, advancing the understanding of complex geometric structures and their transformations.

Contribution

It constructs a new category of polarized twistor D-modules and establishes a Decomposition Theorem within this framework, extending previous theories in complex geometry.

Findings

Proved a Decomposition Theorem for direct images of irreducible local systems.

Constructed a category of polarized twistor D-modules.

Extended decomposition results to a new categorical setting.

Abstract

We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category of polarized twistor D-modules and show a Decomposition Theorem in this category.