论文标题
区分siegel模块化表单和$ {\ mathcal a} _g $的移动斜率
Differentiating Siegel modular forms, and the moving slope of ${\mathcal A}_g$
论文作者
论文摘要
我们研究了Moduli空间上移动除数的锥，$ {\ Mathcal a} _g $主要是极化的Abelian品种。我们构建了一个非线性全态差分运算符，部分是由广义的兰金·科恩支架激励的，该操作员将Siegel模块化形式发送给Siegel模块化形式，并将其应用于产生新的模块化形式。我们的构造收回了$ {\ Mathcal a} _g $ for $ g \ leq 4 $上的最小移动斜率的已知分隔线，并为$ {\ Mathcal a} _5 $的移动斜率和$ {$ {$ {$ {\ Mathscal的移动坡度均具有明确的上限。
We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms. Our construction recovers the known divisors of minimal moving slope on ${\mathcal A}_g$ for $g\leq 4$, and gives an explicit upper bound for the moving slope of ${\mathcal A}_5$ and a conjectural upper bound for the moving slope of ${\mathcal A}_6$.
