Modularity of d $d$ -elliptic loci with level structure

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-06-25 DOI:10.1112/jlms.70212

François Greer, Carl Lian

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引用次数: 0

Abstract

We consider the generating series of special cycles on $A_{1} (N) \times A_{g} (N)$ , with full level $N$ structure, valued in the cohomology of degree $2 g$ . The modularity theorem of Kudla–Millson for locally symmetric spaces implies that these series are modular. When $N = 1$ , the images of these loci in $A_{g}$ are the $d$ -elliptic Noether–Lefschetz loci, which are conjectured to be modular. In the Appendix, it is shown that the resulting modular forms are nonzero for $g = 2$ when $N ⩾ 11$ and $N \neq 12$ .

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考虑a1 (N) × a1 (N)上的特殊环的生成级数$\mathcal {A}_1(N)\times \mathcal {A}_g(N)$，具有全N阶$N$结构，值为2g次上同调$2g$。局部对称空间的Kudla-Millson模定理表明这些级数是模的。当N = 1 $N=1$时，这些基因座在A g $\mathcal {A}_g$中的图像为d $d$ -椭圆Noether-Lefschetz基因座，推测其为模。在附录中，结果表明，当N大于或等于11 $N\geqslant 11$且N≠12 $N\ne 12$时，所得到的模形式对于g = 2 $g=2$是非零的。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.