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- Title
The Noether-Lefschetz conjecture and generalizations.
- Authors
Bergeron, Nicolas; Li, Zhiyuan; Millson, John; Moeglin, Colette
- 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 [3], here we extend the results of [3] to non-compact manifolds. This allows us to apply our results to the moduli spaces of quasi-polarized K3 surfaces.
- Subjects
MODULI theory; TOPOLOGICAL spaces; ORTHOGONAL surfaces; MANIFOLDS (Mathematics); GENERALIZATION
- Publication
Inventiones Mathematicae, 2017, Vol 208, Issue 2, p501
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-016-0695-z