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Betti tables of reducible algebraic curves


Authors: David J. Bruce, Pin-Hung Kao, Evan D. Nash, Ben Perez and Peter Vermeire
Journal: Proc. Amer. Math. Soc. 142 (2014), 4039-4051
MSC (2010): Primary 13D02; Secondary 14N05, 14H99, 14N20, 14Q05
DOI: https://doi.org/10.1090/S0002-9939-2014-12158-7
Published electronically: August 14, 2014
MathSciNet review: 3266976
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses. We also give explicit formulas for the entries of the Betti tables for all curves of genus zero and one. Last, we give formulas for the graded Betti numbers for a class of curves of higher genus.


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Additional Information

David J. Bruce
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: djbruce@umich.edu

Pin-Hung Kao
Affiliation: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859
Email: kao1p@cmich.edu

Evan D. Nash
Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
Email: e{\textunderscore}nash@cox.net

Ben Perez
Affiliation: Department of Mathematics, St. Olaf College, Northfield, Minnesota 55057
Email: perez@stolaf.edu

Peter Vermeire
Affiliation: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859
Email: p.vermeire@cmich.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12158-7
Received by editor(s): October 17, 2012
Received by editor(s) in revised form: January 24, 2013
Published electronically: August 14, 2014
Additional Notes: The first, third, and fourth authors were supported by NSF grant DMS-1156890.
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society