  In this paper, the Euler characteristic formula for projective logarithmic
minimal degenerations of surfaces with Kodaira dimension zero over a
1-dimensional complex disk is proved under a reasonable assumption and as its
application, the singularity of logarithmic minimal degenerations are
determined in the abelian or hyperelliptic case. By globalizing this local
analysis of singular fibres via generalized canonical bundle formulae due to
Fujino-Mori, we bound the number of singular fibres of abelian fibred
Calabi-Yau threefolds from above,which was previously done by Oguiso in the
potentially good reduction case.
