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arXiv · 1412.3774

The Noether-Lefschetz conjecture and generalizations

Nicolas Bergeron·Zhiyuan Li·John Millson·Colette Moeglin
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Abstract

We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. For compact manifolds this was proved in \cite{BMM11}, here we extend the results of \cite{BMM11} to non-compact manifolds. This allows us to apply our results to the moduli spaces of quasi-polarized K3 surfaces.

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Nicolas Bergeron, Zhiyuan Li, John Millson, Colette Moeglin. 2014-12-11. The Noether-Lefschetz conjecture and generalizations. https://arxiv.org/abs/1412.3774

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