On compact complex surfaces of K\"ahler rank one
Complex Variables
2010-10-14 v1 Algebraic Geometry
Abstract
The K\"ahler rank of compact complex surfaces was introduced by Harvey and Lawson in their 1983 paper on K\"ahler manifolds as a measure of ``k\"alerianity''. Here we give a partial classification of compact complex surfaces of K\"ahler rank 1. These are either elliptic surfaces, or Hopf surfaces, or they admit a holomorphic foliation of a very special type. As a consequence we give an affirmative answer to the question raised by Harvey and Lawson whether the K\"ahler rank is a birational invariant.
Keywords
Cite
@article{arxiv.1010.2591,
title = {On compact complex surfaces of K\"ahler rank one},
author = {Ionut Chiose and Matei Toma},
journal= {arXiv preprint arXiv:1010.2591},
year = {2010}
}
Comments
Submitted to Amer. J. Math