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VOL. 12 | 2011 Modular Forms on Ball Quotients of Non-Positive Kodaira Dimension
Azniv Kasparian

Editor(s) Ivaïlo M. Mladenov, Gaetano Vilasi, Akira Yoshioka


The Baily-Borel compactification $\widehat{{\mathbb B} / \Gamma}$ of an arithmetic ball quotient admits projective embeddings by $\Gamma$-modular forms of sufficiently large weight. We are interested in the target and the rank of the projective map $\Phi$, determined by $\Gamma$-modular forms of weight one. This paper concentrates on the finite $H$-Galois quotients ${\mathbb B} / \Gamma _H$ of a specific ${\mathbb B} / \Gamma _{-1}^{(6,8)}$, birational to an abelian surface $A_{-1}$. Any compactification of ${\mathbb B} / \Gamma _H$ has non-positive Kodaira dimension. The rational maps $\Phi ^H$ of $\widehat{{\mathbb B} / \Gamma _H}$ are studied by means of the $H$-invariant abelian functions on $A_{-1}$.


Published: 1 January 2011
First available in Project Euclid: 13 July 2015

zbMATH: 1382.32016
MathSciNet: MR2780242

Digital Object Identifier: 10.7546/giq-12-2011-263-289

Rights: Copyright © 2011 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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