Applications of principal isogenies to constructions of ball quotient surfaces

Abstract

Let $((\mathbb{B}/{\Gamma }_1{)}^{\prime },T(1))$ be á torsion free toroidal compactification with abelian minimal model $(A_1,D(1))$. An arbitrary principal isogeny ${\mu }_a:A_2\to A_1$, $a\in \mathbb{C}$ pulls-back $(A_1,D(1))$ to the abelian minimal model $(A_2,D(2))$ of a torsion free toroidal compactification $((\mathbb{B}/{\Gamma }_2{)}^{\prime },D(2))$. 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 $((\mathbb{B}/{\Gamma }_n{)}^{\prime },T(n))$ of a ball quotient compactification $\overline{\mathbb{B}/{\Gamma }_H}$ of Kodaira dimension $\kappa (\overline{\mathbb{B}/{\Gamma }_H})\le 0$. It provides also infinite series of birational models of certain $\mathbb{B}/{\Gamma }_H$.

Thsi paper has been withdrawn, because the setup implies more specific conclusions than the ones, mentioned in the current version

References in corpus (1)

• Galois groups of co-abelian ball quotient covers

Cited by in corpus (1)

• Galois groups of co-abelian ball quotient covers