Compact complex non-K{\"a}hler manifolds associated with totally real reciprocal units

TL;DR

This paper introduces a new class of compact complex non-Kähler manifolds derived from totally real number fields, expanding the understanding of complex geometry in even dimensions.

Contribution

It constructs these manifolds using number theory and explores their analytic and geometric properties, a novel approach in complex geometry.

Findings

Existence of compact complex non-Kähler manifolds in every even dimension.

New connections between number theory and complex geometry.

Insights into the properties of these manifolds.

Abstract

Using the theory of totally real number fields we construct a new class of compact complex non-K{\"a}hler manifolds in every even complex dimension and study their analytic and geometric properties.