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

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