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The Picard scheme
Steven L. Kleiman
We develop in detail most of the theory of the Picard scheme that Grothendieck sketched in two Bourbaki talks and in commentaries on them. Also, we review in brief much of the rest…
The compactified Picard scheme of the compactified Jacobian
Eduardo Esteves, Steven Kleiman
Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the associated Abel map A_L : C -> P, which maps C into its compacti…
Bounding solutions of Pfaff equations
E. Esteves, S. Kleiman
Let ωbe a Pfaff system of differential forms on a projective space. Let S be its singular locus, and Y a solution of ω=0. We prove Y\cap S is of codimension at most 1 in Y, just as…
Bounds on leaves of foliations of the plane
E. Esteves, S. Kleiman
This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex pr…
Bounds on leaves of one-dimensional foliations
E. Esteves, S. Kleiman
Let X be a variety over an algebraically closed field, η:Ω^1_X\to L a one-dimensional singular foliation, and C\subseteq X a projective leaf of η. We prove that 2p_a(C)-2=°(L|C)+λ(…
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…