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• W3096889389 abstract "Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is non-singular, then this rational map is a morphism. As a consequence, we obtain that, if the surface is rational and we fix a divisor class containing a non-singular rational curve, then the scheme parametrizing rational curves on this class is irreducible. Further, if the class has non-negative self-intersection, then the scheme of rational curves has expected dimension." @default.
• W3096889389 created "2020-11-09" @default.
• W3096889389 creator A5081022365 @default.
• W3096889389 date "2020-10-31" @default.
• W3096889389 modified "2023-09-27" @default.
• W3096889389 title "Smooth rational curves on rational surfaces." @default.
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• W3096889389 hasPublicationYear "2020" @default.
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