Abstract

The Kähler rank of compact complex surfaces was introduced by Harvey and Lawson in their 1983 paper on Kähler manifolds as a measure of “kählerianity”. Here we give a partial classification of compact complex surfaces of Kähler 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 Kähler rank is a bimeromorphic invariant.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 851-860
Launched on MUSE
2013-05-30
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.