Bi-Hermitian metrics on Kato 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.

Major revision: we found a gap in the proof of Theorem 5.1 and withdrew it; a few Remarks added

References in corpus (2)

• Twistors and Bi-Hermitian Surfaces of Non-Kähler Type
• Locally conformally symplectic structures on compact non-Kähler complex surfaces