Blowing up generalized Kahler 4-manifolds

TL;DR

This paper demonstrates that generalized Kahler 4-manifolds can be blown up at nondegenerate complex points while preserving a compatible generalized Kahler metric, extending the blow-up operation to bi-Hermitian manifolds.

Contribution

It introduces a blow-up operation for bi-Hermitian manifolds and shows the existence of compatible generalized Kahler metrics after blow-up.

Findings

Blow-up of generalized Kahler 4-manifolds preserves the structure.

The metric can be matched outside a neighborhood of the exceptional divisor.

Develops a new blow-up operation for bi-Hermitian manifolds.

Abstract

We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.