Bi-Hermitian metrics on Kato surfaces

TL;DR

This paper classifies bi-Hermitian metrics on certain compact complex surfaces, providing new examples and a comprehensive understanding of their structure on Kato surfaces and related types.

Contribution

It offers a complete classification of bi-Hermitian metrics on unbranched Kato surfaces and classifies intermediate surfaces up to logarithmic deformation.

Findings

New examples of bi-Hermitian metrics with connected anti-canonical divisor

Complete classification for unbranched Kato surfaces

Classification up to deformation for intermediate surfaces

Abstract

We investigate bi-Hermitian metrics on compact complex surfaces with odd first Betti number producing new examples with connected anti-canonical divisor using the general construction of \cite{abd15}. The result is a complete classification for all \it unbranched \rm Kato surfaces and a classification up to logarithmic deformation for \it intermediate \rm surfaces.