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Enumerating Rational Curves: The Rational Fibration Method

Published online by Cambridge University Press:  04 December 2007

LUCIA CAPORASO
Affiliation:
Mathematics Department, Harvard University, Cambridge MA 02138, USA and Dipartimento di Matematica, Universitá di Roma ‘Tor Vergata‘, Roma 00133, Italy; e-mail: [email protected]
JOE HARRIS
Affiliation:
Mathematics Department, Harvard University, Cambridge MA 02138, USA; e-mail: [email protected]
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Abstract

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A new method to approach enumerative questions about rational curves on algebraic varieties is described. The idea is to reduce the counting problems to computations on the Néron-Severi group of a ruled surface. Applications include a short proof of Kontsevich‘s formula for plane curves and the solution of the analogous problem for the Hirzebruch surface F$_3$.

Type
Research Article
Copyright
© 1998 Kluwer Academic Publishers