Theta functions on the Kodaira-Thurston manifold

TL;DR

This paper introduces theta-function analogues on the Kodaira-Thurston manifold and uses them to embed the manifold into complex projective space, extending classical symplectic and complex geometry concepts.

Contribution

It defines theta-function analogues on the Kodaira-Thurston manifold and constructs a canonical symplectic embedding into complex projective space.

Findings

Successful construction of theta-function analogues

Canonical symplectic embedding into complex projective space

Extension of Lefschetz theorem to this setting

Abstract

We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex projective space (analogue of the Lefshetz theorem).