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math.AG1999
Autoduality of the compactified Jacobian
Eduardo Esteves, Mathieu Gagne, Steven Kleiman
We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map A_L: C…
math.AG1999
Abel Maps and Presentation Schemes
E. Esteves, Mathieu Gagne, S. Kleiman
We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel…
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…