Kasparian, Azniv; Holzapfel, Rolf-Peter Arithmetic proportional elliptic configurations with comparatively large number of irreducible components. (English) Zbl 1158.14311 Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 252-261 (2005). Summary: Let \(T\) be an arithmetic proportional elliptic configuration on a bielliptic 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 \(\text{Aut}(A_{\sqrt{-3}}\)-equivalent to Hirzebruch’s example \(T^{(1,4)}_{\sqrt{-d}}\) with a unique singular point and 4 irreducible components.For the entire collection see [Zbl 1066.53003]. Cited in 1 Document MSC: 14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations 11G15 Complex multiplication and moduli of abelian varieties PDF BibTeX XML Cite \textit{A. Kasparian} and \textit{R.-P. Holzapfel}, in: Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 3--10, 2004. Sofia: Bulgarian Academy of Sciences. 252--261 (2005; Zbl 1158.14311) OpenURL