Reflective modular forms in algebraic geometry
Reflective modular forms in algebraic geometry
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代数几何中的反射模形式
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
V. Gritsenko
中科院分区：
文献类型：
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作者：
V. Gritsenko
我们证明，大权重的强反射模形式的存在意味着相应模变体的小平维数为负，或者在某些特殊情况下等于零。使用雅可比提升，我们用尽可能简单的除数构建了三座强反射模块化形式的塔。特别是，我们获得了 Borcherds-Enriques 模形式 Phi_4 的雅可比提升构造和 Yoshikawa 最近构建的 Del Pezzo 曲面的 K"ahler 模的自守判别式的雅可比提升构造。我们还获得了 Kodaira 维度 0 的 4、6 和 7 维的三个模变体。
We prove that the existence of a strongly reflective modular form of a large weight implies that the Kodaira dimension of the corresponding modular variety is negative or, in some special case, it is equal to zero. Using the Jacobi lifting we construct three towers of strongly reflective modular forms with the simplest possible divisor. In particular we obtain a Jacobi lifting construction of the Borcherds-Enriques modular form Phi_4 and Jacobi liftings of automorphic discriminants of the K"ahler moduli of Del Pezzo surfaces constructed recently by Yoshikawa. We obtain also three modular varieties of dimension 4, 6 and 7 of Kodaira dimension 0.