The Severi problem for rational curves on del Pezzo surfaces 
-- Damiano Testa, March 25, 2005

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Let X be a smooth projective surface and choose a curve C on X. Let
V_C be the set of all irreducible divisors on X linearly equivalent to
C whose normalization is a rational curve. The Severi problem for
rational curves on X with divisor class [C] consists of studying the
irreducibility of the spaces V_C as C varies among all curves on X.

In this talk, we will prove that all the spaces V_C are irreducible in
the case where X is a del Pezzo surface, with a unique exception.