Limit linear series for curves not of compact type
Abstract
We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding specialization result. For a more restricted class of curves which simultaneously generalizes two-component curves and curves of compact type, we give an equivalent definition of limit linear series, which is visibly a generalization of the Eisenbud-Harris definition. Finally, for the same class of curves, we prove a smoothing theorem which constitutes an improvement over known results even in the compact-type case.
Keywords
Cite
@article{arxiv.1406.6699,
title = {Limit linear series for curves not of compact type},
author = {Brian Osserman},
journal= {arXiv preprint arXiv:1406.6699},
year = {2014}
}
Comments
34 pages, 1 figure. v2: added smoothing theorem, and proposition on independence of choice of concentrated multidegrees. v3: minor revisions, primarily for compatibility with [MO]