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math.AG2001
Node polynomials for families: results and examples
S. Kleiman, R. Piene
We continue the development of methods for enumerating nodal curves on smooth complex surfaces, stressing the range of validity. We illustrate the new methods in three important ex…
math.AG1999
Enumerating singular curves on surfaces
Steven Kleiman, Ragni Piene
We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may h…