JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 1, Pages 53 - 84
(April 2003)
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RATIONAL CURVES ON RATIONAL SURFACES
Fumio Hazama (Japan)
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Abstract: Let S
be a projective surface and d be a
positive integer. Let
be the number of algebraic equivalence
classes of rational curves of degree d,
and let
be its generating function. The purpose of
this paper is to show that
is a rational function in x for a class
of rational surfaces including Del Pezzo
surfaces and Hirzebruch surfaces. |
Keywords and phrases: rational surface, rational curve. |
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