Applications of principal isogenies to constructions of ball quotient surfaces

Azniv Kasparian

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arXiv · 1201.0093

Applications of principal isogenies to constructions of ball quotient surfaces

Azniv Kasparian

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Abstract

Let $(({\mathbb B} / Γ_1)', T(1))$ be á torsion free toroidal compactification with abelian minimal model $(A_1, D(1))$. An arbitrary principal isogeny $μ_a : A_2 \rightarrow A_1$, $a \in {\mathbb C}$ pulls-back $(A_1, D(1))$ to the abelian minimal model $(A_2, D(2))$ of a torsion free toroidal compactification $(({\mathbb B} / Γ_2)', D(2))$. 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 $(({\mathbb B} / Γ_n)', T(n))$ of a ball quotient compactification $\bar{{\mathbb B} / Γ_H}$ of Kodaira dimension $κ(\bar{{\mathbb B} / Γ_H}) \leq 0$. It provides also infinite series of birational models of certain ${\mathbb B} / Γ_H$.

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BibTeX RIS

Azniv Kasparian. 2012-05-30. Applications of principal isogenies to constructions of ball quotient surfaces. https://arxiv.org/abs/1201.0093

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