标题： 主同构的应用到球商曲面的构造中 显示英文标题

标题： Applications of principal isogenies to constructions of ball quotient surfaces

摘要： 设 $(({\mathbb B} / \Gamma_1)', T(1))$ 为具有 Abel 最小模型 $(A_1, D(1))$ 的无挠 toroidal紧致化。任意主同态 $\mu_a : A_2 \rightarrow A_1$，$a \in {\mathbb C}$ 将 $(A_1, D(1))$ 拉回到无挠 toroidal紧致化的 Abel 最小模型 $(A_2, D(2))$ 上，该紧致化为 $(({\mathbb B} / \Gamma_2)', D(2))$。 本工作利用阿贝尔双曲商模型的同态逆像，构造了球面商紧致化 $\bar{{\mathbb B} / \Gamma_H}$ （Kodaira维数为 $\kappa (\bar{{\mathbb B} / \Gamma_H}) \leq 0$）的无穷多组彼此非双有理共轭自由Galois覆盖 $(({\mathbb B} / \Gamma_n)', T(n))$。同时，还提供了某些 ${\mathbb B} / \Gamma_H$ 的无穷多组双有理模型。 显示英文摘要

摘要： Let $(({\mathbb B} / \Gamma_1)', T(1))$ be \'a torsion free toroidal compactification with abelian minimal model $(A_1, D(1))$. An arbitrary principal isogeny $\mu_a : A_2 \rightarrow A_1$, $a \in {\mathbb C}$ pulls-back $(A_1, D(1))$ to the abelian minimal model $(A_2, D(2))$ of a torsion free toroidal compactification $(({\mathbb B} / \Gamma_2)', D(2))$. The present work makes use of the isogeny pull-backs of abelian ball quotient models, towards the construction of infinite series of mutually non-birational co-abelian torsion free Galois covers $(({\mathbb B} / \Gamma_n)', T(n))$ of a ball quotient compactification $\bar{{\mathbb B} / \Gamma_H}$ of Kodaira dimension $\kappa (\bar{{\mathbb B} / \Gamma_H}) \leq 0$. It provides also infinite series of birational models of certain ${\mathbb B} / \Gamma_H$.