Vector valued modular forms and the modular orbifold of elliptic curves
Vector valued modular forms and the modular orbifold of elliptic curves
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向量值模形式和椭圆曲线的模环折
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. Franc
中科院分区：
文献类型：
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作者：
L. Candelori;C. Franc
本文从几何角度提出了全纯向量值模形式的理论。更准确地说，我们在广义椭圆曲线的模轨道上定义某些全纯向量丛，其截面是向量值模形式。这种观点简化了理论，并阐明了 SL_2(Z) 表示的指数在向量值模形式的全纯理论中所起的作用。此外，它允许人们使用代数几何中的标准技术，通过用加权投影线 P(4, 6) 识别模轨道来推导自由模定理和维数公式（之前由其他作者使用不同技术推导）。
This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular orbifold of generalized elliptic curves whose sections are vector valued modular forms. This perspective simplifies the theory, and it clarifies the role that exponents of representations of SL_2(Z) play in the holomorphic theory of vector valued modular forms. Further, it allows one to use standard techniques in algebraic geometry to deduce free-module theorems and dimension formulae (deduced previously by other authors using different techniques), by identifying the modular orbifold with the weighted projective line P(4, 6).