Abel maps and limit linear series
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Abel maps and limit linear series

  • Author(s): Esteves, Eduardo
  • Osserman, Brian
  • et al.

Published Web Location

https://arxiv.org/pdf/1102.3191.pdf
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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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