Limit linear series for curves not of compact type

2014/06/25 by Brian Osserman, Osserman, Brian · 2 citations
Mathematics · #14D06 #14H51 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D06 #msc:14H51

paper · pdf · doi:10.48550/arxiv.1406.6699

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]

arxiv created 2014/12/11 · arxiv updated 2014/12/15

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.

Cited by

• Continuous Linear Series
• Polymatroidal tilings and the Chow class of linked projective spaces

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