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arXiv · 0711.1155

L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of Kaehler manifolds

Terrence Napier·Mohan Ramachandran
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Abstract

Simple approaches to the proofs of the L^2 Castelnuovo-de 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 1-forms on a bounded geometry connected complete Kaehler manifold X with v in L^2. According to a version of the L^2 Castelnuovo-de 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 pull-backs. Previous versions required both forms to be in L^2.

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Terrence Napier, Mohan Ramachandran. 2007-11-07. L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of Kaehler manifolds. https://arxiv.org/abs/0711.1155

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