The Euler Characteristic Formula for Logarithmic Minimal Degenerations of Surfaces with Kodaira Dimension Zero and its application to Calabi-Yau Threefolds with a pencil

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 determin...

Full description

Saved in:
Bibliographic Details
Main Author Ohno, Koji
Format Journal Article
LanguageEnglish
Published 19.10.2007
Subjects
Mathematics - Algebraic Geometry
Online AccessGet full text

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.0710.3641