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Linked determinantal loci and limit linear series


Authors: John Murray and Brian Osserman
Journal: Proc. Amer. Math. Soc. 144 (2016), 2399-2410
MSC (2010): Primary 14D06, 14H57, 14M12
Published electronically: November 20, 2015
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Abstract: 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.


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Additional Information

John Murray
Affiliation: Department of Mathematics, University of California, Davis, One Shields Ave., Davis, California 95616

Brian Osserman
Affiliation: Department of Mathematics, University of California, Davis, One Shields Ave., Davis, California 95616

DOI: https://doi.org/10.1090/proc/12965
Received by editor(s): December 11, 2014
Received by editor(s) in revised form: July 13, 2015, and July 30, 2015
Published electronically: November 20, 2015
Additional Notes: The second author was partially supported by Simons Foundation grant #279151 during the preparation of this work.
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society