The Noether-Lefschetz conjecture and generalizations
Algebraic Geometry
2015-04-15 v2 Number Theory
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.
Cite
@article{arxiv.1412.3774,
title = {The Noether-Lefschetz conjecture and generalizations},
author = {Nicolas Bergeron and Zhiyuan Li and John Millson and Colette Moeglin},
journal= {arXiv preprint arXiv:1412.3774},
year = {2015}
}