Abstract
Surfaces whose prime (i.e. hyperplane) sections are hyperelliptic were studied and classified by Castelnuovo (2). If the sections have genus p, no surface can have order greater than 4p + 4, and any of lesser order is a projection of a normal surface Ф in a projective space S of 3p + 5 dimensions. There is a pencil of conies, none of them singular, on Ф; through each point of Ф passes one of the conies and their planes generate a threefold V of order 3p + 3 (2, § as the paper was later republished with different pagination, it may be advisable to refer to it by sections).
An addendum to Castelnuovo.
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References
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© 1981 Springer-Verlag New York Inc.
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Edge, W.L. (1981). Algebraic Surfaces with Hyperelliptic Sections. In: Davis, C., Grünbaum, B., Sherk, F.A. (eds) The Geometric Vein. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5648-9_24
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DOI: https://doi.org/10.1007/978-1-4612-5648-9_24
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