The Noether-Lefschetz conjecture and generalizations
By Nicolas Bergeron, Zhiyuan Li, John Millson, C. Moeglin. 2014
50 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4d52432b175f6cec643b6df59c264610546029d9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- D. Oprea
- R. Pandharipande
- A. Marian
- D. Huybrechts
- Richard P. Thomas
- Yukinobu Toda
- A. Okounkov
- Aaron Pixton
In Mathematical Physics
- R. Pandharipande
- D. Oprea
- A. Marian
- D. Huybrechts
- Richard P. Thomas
- Aaron Pixton
- A. Okounkov
- Davesh Maulik
Citations in the corpus
- Lectures on K3 Surfaces (2016, background): “Li and Tian in [359] and, more generally, Bergeron et al in [58] prove that Pic(M̄d) ' H(2)(M̄d,Q) for all d and that the Noether–Lefschetz divisors generate the cohomology.”
- Segre classes and Hilbert schemes of points (2015, methodology): “oci define classes in the Chow ring A⋆(M2ℓ,Q). Let NL⋆(M 2ℓ) ⊂ A ⋆(M 2ℓ,Q) be the subalgebra generated by Noether-Lefschetz loci (of all codimensions). A basic result conjectured in [18] and proven in [3] is the isomorphism NL1(M 2ℓ) = A 1(M 2ℓ,Q). Another method of constructing classes in A⋆(M2ℓ,Q) ”