The algebra of closed forms in a disk is Koszul

TL;DR

This paper proves that the algebra of closed differential forms with logarithmic singularities in a disk is Koszul, linking it to mixed Hodge-Tate structures, and discusses both algebraic and topological aspects.

Contribution

It establishes the Koszul property of the algebra of closed forms with logarithmic singularities, connecting it to mixed Hodge-Tate structures, which is a novel result.

Findings

The algebra of closed forms in a disk is Koszul.

The result holds in algebraic, formal, and analytic contexts.

Connection to variations of mixed Hodge-Tate structures is discussed.

Abstract

We prove that the algebra of closed differential forms in an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is (both nontopologically and topologically) Koszul. The connection with variations of mixed Hodge-Tate structures, based on a preprint by Andrey Levin, is discussed in the introduction.