The surfaces whose prime-sections contain a
1934 ◽
Vol 30
(2)
◽
pp. 170-177
◽
Keyword(s):
The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.
1994 ◽
pp. 211-220
2017 ◽
Vol 49
(3)
◽
pp. 69-77
1973 ◽
Vol 29
(4)
◽
pp. 76-77
2015 ◽
Vol 18
(1)
◽
pp. 258-265
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Keyword(s):
Keyword(s):