Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Esteves, Eduardo, Osserman, Brian
Institution: Instituto Nacional de Matemática Pura e Aplicada
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952328443