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2010 Modular Forms on Ball Quotients of Non-Positive Kodaira Dimension
Azniv Kasparian
J. Geom. Symmetry Phys. 20: 69-96 (2010). DOI: 10.7546/jgsp-20-2010-69-96


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 $A_{-1}$.


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Azniv Kasparian. "Modular Forms on Ball Quotients of Non-Positive Kodaira Dimension." J. Geom. Symmetry Phys. 20 69 - 96, 2010.


Published: 2010
First available in Project Euclid: 25 May 2017

zbMATH: 1268.32006
MathSciNet: MR2780242
Digital Object Identifier: 10.7546/jgsp-20-2010-69-96

Rights: Copyright © 2010 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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