论文标题
Mathieu Moonshine和Borcherds产品
Mathieu moonshine and Borcherds products
论文作者
论文摘要
$ K3 $表面的扭曲椭圆属与Mathieu组的共轭类$ M_ {24} $相关的类别是弱的Jacobi重量$ 0 $。 2010年，Cheng从扭曲的椭圆属中构建了形式的无限产物，并猜想它们定义了第二级的Siegel模块化形式。在本文中，我们证明，对于lattice $ u（n_g）\ oplus u \ oplus u \ oplus a_1 $的每个级别$ n_g $的共轭类是一种相关产品。我们还计算了这些产品的除数，并确定该产品可以将产品实现为添加剂（广义saito-kurokawa）升力。
The twisted elliptic genera of a $K3$ surface associated with the conjugacy classes of the Mathieu group $M_{24}$ are known to be weak Jacobi forms of weight $0$. In 2010, Cheng constructed formal infinite products from the twisted elliptic genera and conjectured that they define Siegel modular forms of degree two. In this paper we prove that for each conjugacy class of level $N_g$ the associated product is a meromorphic Borcherds product on the lattice $U(N_g)\oplus U \oplus A_1$ in a strict sense. We also compute the divisors of these products and determine for which conjugacy classes the product can be realized as an additive (generalized Saito--Kurokawa) lift.
