Open Access
VOL. 6 | 2005 Arithmetic Proportional Elliptic Configurations with Comparatively Large Number of Irreducible Components
Azniv Kasparian, Rolf-Peter Holzapfel

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2005: 252-261 (2005) DOI: 10.7546/giq-6-2005-252-261


Let $T$ be an arithmetic proportional elliptic configuration on a bi-elliptic surface $A \sqrt{-d}$ with complex multiplication by an imaginary quadratic number field $\mathbb{Q}(\sqrt{-d})$. The present note establishes that if $T$ has $s$ singular points and \[ 4s − 5 \leq h \leq 4s \] irreducible smooth elliptic components, then $d = 3$ and $T$ is $\mathrm{Aut}(A \sqrt{-3}−$ equivalent to Hirzebruch’s example $T^{(1,4)}_{\sqrt{-3}}$ with a unique singular point and 4 irreducible components.


Published: 1 January 2005
First available in Project Euclid: 12 June 2015

zbMATH: 1158.14311
MathSciNet: MR2161772

Digital Object Identifier: 10.7546/giq-6-2005-252-261

Rights: Copyright © 2005 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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