论文标题
来自镜子对称性的准模块形式的衍生代数
The algebra of derivations of quasi-modular forms from mirror symmetry
论文作者
论文摘要
我们研究了镜面非紧密calabi-yau的模量空间，并通过差异形式的选择增强了三倍。差异形式是中维的元素，其变异是由配备平坦高斯 - 曼宁连接的混合杂货结构的变化来描述的。我们在这些模量空间上构建特殊功能的分级差分环，并表明它们包含准模块化形式的环。我们表明，可以从与增强的模量空间上的矢量场收缩的高斯 - 曼宁连接获得准模块形式的代数。我们提供了由$ \ mathbb {p}^2 $和$ \ mathbb {f} _2 $的规范捆绑包的镜子给出的示例。
We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed Hodge structures which is equipped with a flat Gauss-Manin connection. We construct graded differential rings of special functions on these moduli spaces and show that they contain rings of quasi-modular forms. We show that the algebra of derivations of quasi-modular forms can be obtained from the Gauss--Manin connection contracted with vector fields on the enhanced moduli spaces. We provide examples for this construction given by the mirrors of the canonical bundles of $\mathbb{P}^2$ and $\mathbb{F}_2$.
