Examples of non-commutative Hodge structures

TL;DR

This paper establishes a criterion linking the positivity of the Stokes matrix in certain connections to the purity and polarization of associated non-commutative Hodge structures, advancing understanding in complex geometry.

Contribution

It provides a new condition involving the Stokes matrix that guarantees the purity and polarization of non-commutative Hodge structures.

Findings

Positivity of the combined Stokes matrix implies pure and polarized structures.

Connects Stokes matrix properties to geometric structures in complex analysis.

Enhances criteria for non-commutative Hodge theory applications.

Abstract

We show that if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, then the associated integrable twistor structure (or TERP structure, or non-commutative Hodge structure) is pure and polarized.