Correction to “Combinatorics and geometry of power ideals”: Two counterexamples for power ideals of hyperplane arrangements
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- by Federico Ardila and Alexander Postnikov PDF
- Trans. Amer. Math. Soc. 367 (2015), 3759-3762 Request permission
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 $k \leq -6$.References
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Additional Information
- Federico Ardila
- Affiliation: Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94110
- MR Author ID: 725066
- 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
- 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. - © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3314823