Speciality one rational surfaces in P4

1992 ◽  
pp. 1-23 ◽  
Author(s):  
J. Alexander
Keyword(s):  
Rational Surfaces

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

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.

scholarly journals Implicitization of rational surfaces using toric varieties

2006 ◽  
Vol 303 (2) ◽  
pp. 543-565 ◽  
Author(s):  
Amit Khetan ◽  
Carlos D'Andrea
Keyword(s):  
Toric Varieties ◽  
Rational Surfaces
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