Erratum to: On Bi-Hermitian Surfaces
Erratum to: Chapter 15 in: D. Angella, C. Medori & A. Tomassini (eds.), Complex and Symplectic Geometry, https://doi.org/10.1007/978-3-319-62914-8_15
The author found an error in the original version of the chapter. This error affected also his contribution to the book and hence the author wanted to publish the below disclaimer by this erratum.
We found a gap in the proof of Theorem 3.4, as a result we do not know if the statement is correct.
The problem with the proof is that when S u is a small deformation of a hyperbolic Inoue surface S0 the inequality H0(S u , K−1L v ) ≠ 0 certainly holds but deg L v > 0 by [18, 4.21, 4.22] and therefore Theorem 3.2 does not apply.