Archiv der Mathematik

, Volume 105, Issue 4, pp 343–349 | Cite as

Star configurations are set-theoretic complete intersections



Let \({\mathcal{A} \subset \mathbb P^{k-1}}\) be a rank k arrangement of n hyperplanes, with the property that any k of the defining linear forms are linearly independent (i.e., \({\mathcal{A}}\) is called k-generic). We show that for any \({j=0,\ldots,k-2}\), the subspace arrangement with defining ideal generated by the (nj)-fold products of the defining linear forms of \({\mathcal{A}}\) is a set-theoretic complete intersection, which is equivalent to saying that star configurations have this property.

Mathematics Subject Classification

Primary 14N20 Secondary 16N40 


Star configuration Set-theoretic complete intersection 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IdahoMoscowUSA

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