2014/12/11 by John Murray, Murray, John, Brian Osserman +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1412.3818
11 pages
arxiv created 2014/12/11 · arxiv updated 2014/12/15
We study (a generalization of) the notion of linked determinantal loci recently introduced by the second author, showing that as with classical determinantal loci, they are Cohen-Macaulay whenever they have the expected codimension. We apply this to prove Cohen-Macaulayness and flatness for moduli spaces of limit linear series, and to prove a comparison result between the scheme structures of Eisenbud-Harris limit linear series and the spaces of limit linear series recently constructed by the second author. This comparison result is crucial in order to study the geometry of Brill-Noether loci via degenerations.