The Noether-Lefschetz conjecture and generalizations

被引：21
|
作者：
Bergeron, Nicolas [1 ]
Li, Zhiyuan [2 ]
Millson, John [3 ]
Moeglin, Colette [4 ]
机构：
[1] Univ Paris Diderot, UPMC Univ Paris 06, Sorbonne Univ,Sorbonne Paris Cite, Inst Math Jussieu Paris Rive Gauche,CNRS,UMR 7586, 4 Pl Jussieu, F-75005 Paris, France
[2] Fudan Univ, Shanghai Ctr Math Sci, Handan Rd 220,Guanghua East Tower, Shanghai 200433, Peoples R China
[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA
[4] Univ Paris Diderot, UPMC Univ Paris 06, Sorbonne Univ,Sorbonne Paris Cite, Inst Math Jussieu Paris Rive Gauche,CNRS,UMR7586, 4 Pl Jussieu, F-75005 Paris, France
来源：
INVENTIONES MATHEMATICAE | 2017年 / 208卷 / 02期
关键词：
K3; SURFACES; ARITHMETIC QUOTIENTS; FUNDAMENTAL LEMMA; AUTOMORPHIC-FORMS; PICARD-GROUPS; K-3; MODULI SPACE; VARIETIES; REPRESENTATIONS; PRODUCTS;
D O I：
10.1007/s00222-016-0695-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：501 / 552
页数：52
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