Abstract
We explore the relationship between limit linear series and fibers of Abel maps in the case of curves with two smooth components glued at a single node. To an $$r$$ -dimensional limit linear series satisfying a certain exactness property (weaker than the refinedness property of Eisenbud and Harris) we associate a closed subscheme of the appropriate fiber of the Abel map. We then describe this closed subscheme explicitly, computing its Hilbert polynomial and showing that it is Cohen–Macaulay of pure dimension $$r$$ . We show that this construction is also compatible with one-parameter smoothings.
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