On the de Rham complex of mixed twistor D-modules

TL;DR

This paper introduces a new t-structure on derived categories of constructible complexes over complex manifolds and proves the perverse nature of the de Rham complex for certain mixed twistor D-modules, advancing understanding in complex geometry.

Contribution

It defines a novel t-structure on derived categories for complex manifolds and establishes the perverse property of de Rham complexes in the context of mixed twistor D-modules.

Findings

De Rham complex of certain D-modules is perverse relative to the new t-structure.

The t-structure applies to mixed twistor D-modules, broadening their analytical framework.

The results connect complex geometry, D-module theory, and perverse sheaves.

Abstract

Given a complex manifold S, we introduce for each complex manifold X a t-structure on the bounded derived category of C-constructible complexes of O_S-modules on X x S. We prove that the de Rham complex of a holonomic D_{XxS/S}-module which is O_S-flat as well as its dual object is perverse relatively to this t-structure. This result applies to mixed twistor D-modules.