Generalized complex structures on Kodaira surfaces

TL;DR

This paper analyzes the deformations of generalized complex structures on primary Kodaira surfaces, showing a smooth family of deformations parameterized by four complex parameters, aligning with previous extended deformation results.

Contribution

It explicitly computes the deformation space of generalized complex structures on Kodaira surfaces and connects it with known extended deformation frameworks.

Findings

Deformation family depends on four complex parameters.

Deformation family is smooth and locally complete.

Matches extended deformation results by Poon.

Abstract

We compute the deformations in the sense of generalized complex structures of the standard classical complex structure on a primary Kodaira surface and we prove that the obtained family of deformations is a smooth locally complete family depending on four complex parameters. This family is the same as the extended deformations (in the sense of Kontsevich and Barannikov) in degree two, obtained by Poon using differential Gerstenhaber algebras.