Moduli Space of Elliptic Curves with Heisenberg Level Structure
Moduli Space of Elliptic Curves with Heisenberg Level Structure
复制标题
海森堡能级结构的椭圆曲线模空间
DOI：
10.1007/978-3-0348-8303-0_11
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Terasoma
中科院分区：
文献类型：
--
作者：
I. Nakamura;T. Terasoma
椭圆曲线上的Heisenberg能级结构是非对易Heisenberg群在线丛的整体截面空间上的线性作用的一种标记。如果极化度等于d≥3，则具有海森堡能级结构的极化椭圆曲线的模方案是上的拟射影曲线.我们证明了它同构于经典意义下具有水平d结构的椭圆曲线的模方案X(D)的开子格式.此外，我们还证明了当模为奇数时，模上的万能曲线与X(D)上的万能曲线相同，即使它们是不同的。特别地，环SQ0(D)上的泛椭圆曲线对于d≥4甚至偶数都没有全局截线。
A Heisenberg level structure on an elliptic curve is a kind of marking of the linear action by thenoncommutativeHeisenberg group on the space of global sections of a line bundle. The moduli scheme of polarized elliptic curves with Heisenberg level structures is known to be a quasi projective curve overif the degree of polarization is equal to d ≥3. We prove that it is isomorphic to the (open subscheme of the) moduli schemeX(d)of elliptic curves with level d-structures in the classical sense. Moreover, we also prove that the universal curve over the moduli is the same as that overX(d)ifdis odd, while they are different fordeven. In particular, the universal elliptic curve overSQ0(d) has no global sections for d ≥ 4 and even.