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Correction to ``Combinatorics and geometry of power ideals'': Two counterexamples for power ideals of hyperplane arrangements


Authors: Federico Ardila and Alexander Postnikov
Journal: Trans. Amer. Math. Soc. 367 (2015), 3759-3762
MSC (2010): Primary 05A15, 05B35, 13P99, 41A15, 52C35
DOI: https://doi.org/10.1090/S0002-9947-2015-06071-1
Published electronically: January 15, 2015
Original Article: Trans. Amer. Math. Soc. 362 (2010), 4357-4384.
MathSciNet review: 3314823
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Abstract: We disprove Holtz and Ron's conjecture that the power ideal $ C_{\mathcal {A},-2}$ of a hyperplane arrangement $ \mathcal {A}$ (also called the internal zonotopal space) is generated by $ \mathcal {A}$-monomials. We also show that, in contrast with the case $ k \geq -2$, the Hilbert series of $ C_{\mathcal {A},k}$ is not determined by the matroid of $ \mathcal {A}$ for $ k \leq -6$.


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Additional Information

Federico Ardila
Affiliation: Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94110
Email: federico@sfsu.edu

Alexander Postnikov
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: apost@math.mit.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06071-1
Received by editor(s): November 7, 2012
Received by editor(s) in revised form: January 4, 2013
Published electronically: January 15, 2015
Additional Notes: The first author was supported in part by NSF Award DMS-0801075 and CAREER Award DMS-0956178.
The second author was supported in part by NSF CAREER Award DMS-0504629.
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.