Algebraic Surfaces with Hyperelliptic Sections

W. L. Edge
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W. L. Edge: Inveresk House

A chapter in The Geometric Vein, 1981, pp 335-344 from Springer

Abstract: 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).

Keywords: Projective Space; Tangent Space; Algebraic Surface; Pezzo Surface; Prime Section (search for similar items in EconPapers)
Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5648-9_24

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DOI: 10.1007/978-1-4612-5648-9_24

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