L^2 Castelnuovode Franchis, the cup product lemma, and filtered ends of Kaehler manifolds
Abstract
Simple approaches to the proofs of the L^2 Castelnuovode Franchis theorem and the cup product lemma which give new versions are developed. For example, suppose u and v are two linearly independent closed holomorphic 1forms on a bounded geometry connected complete Kaehler manifold X with v in L^2. According to a version of the L^2 Castelnuovode Franchis theorem obtained in this paper, if u and v are pointwise linearly dependent, then there exists a surjective proper holomorphic mapping of X onto a Riemann surface for which u and v are pullbacks. Previous versions required both forms to be in L^2.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1155
 Bibcode:
 2007arXiv0711.1155N
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Complex Variables;
 32Q15