Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations
Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations
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模形式、穿孔球体的变形以及对称张量表示的扩展
DOI：
10.4310/mrl.2023.v30.n5.a2
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发表时间：
2020
影响因子：
1
通讯作者：
G. Bogo
中科院分区：
文献类型：
--
作者：
G. Bogo
设~$X=\Po/\Gamma$是~$n$-穿孔球面，$n>；3$.基于经典的微分方程化理论和辅助参数理论，我们在模形式空间~$M_*(\Gamma)$上引入并研究了~$n-3$形变算子。当限制到模函数时，我们恢复了Teichm-Uller理论中与~$X$的复结构的变形有关的一个结构.我们用相对于四重尖点形式的Eichler积分的导子和对称张量表示的扩张所附的矢量值的模形式来描述变形算子.
Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory parameters. When restricting to modular functions, we recover a construction in Teichm\"uller theory related to the deformation of the complex structure of~$X$. We describe the deformation operators in terms of derivations with respect to Eichler integrals of weight-four cusp forms, and in terms of vector-valued modular forms attached to extensions of symmetric tensor representations.