Veech, William A. Geometric realizations of hyperelliptic curves. II. (English) Zbl 0952.30037 Dani, S. G. (ed.), Lie groups and ergodic theory. Proceedings of the international colloquium, Mumbai, India, January 4-12, 1996. New Delhi: Narosa Publishing House. Stud. Math., Tata Inst. Fundam. Res. 14, 345-365 (1998). The differential equation for the Weierstrass function \(\wp(z)\) exhibits a biholomorphism between the complex 2-manifold \(\mathcal L\) of lattices in \(\mathbb C\) and the set \(\mathcal C\) of cubic polynomial \(q(z)=4z^3-g_2z-g_3\) such that \(g_2^3-27g_3^2\neq 0.\) The author introduces the corresponding complex \(2p\)-manifolds, \(\mathcal L_p\) and \(\mathcal C_p\), \(p\geq 1,\) so that the above statement is generalized in the context of hyperelliptic curves of genus \(p.\) For part I see the author in Proc. Hayashibara Forum 92, New York, NY: Plenum Press. 217-226 (1995; Zbl 0859.30039).For the entire collection see [Zbl 0927.00025]. Reviewer: A.V.Chernecky (Odessa) MSC: 30F10 Compact Riemann surfaces and uniformization 14H52 Elliptic curves 14H15 Families, moduli of curves (analytic) Keywords:Weierstrass function; lattices; cubic polynomials; geometric realization of hyperelliptic curves; symmetric \(4p\)-gons; polynomials with nonzero discriminant; biholomorphism; Picard-Fuchs equation; hyperelliptic Riemann surface Citations:Zbl 0859.30039 PDFBibTeX XMLCite \textit{W. A. Veech}, in: Lie groups and ergodic theory. Proceedings of the international colloquium, Mumbai, India, January 4--12, 1996. New Delhi: Narosa Publishing House; Bombay: Tata Institute of Fundamental Research. 345--365 (1998; Zbl 0952.30037)