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Codimension theorems for complete toric varieties

Authors: David Cox and Alicia Dickenstein
Journal: Proc. Amer. Math. Soc. 133 (2005), 3153-3162
MSC (2000): Primary 14M25
Published electronically: May 2, 2005
MathSciNet review: 2160176
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Abstract: Let $X$ be a complete toric variety with homogeneous coordinate ring $S$. In this article, we compute upper and lower bounds for the codimension in the critical degree of ideals of $S$ generated by $\dim(X)+1$ homogeneous polynomials that do not vanish simultaneously on $X$.

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Additional Information

David Cox
Affiliation: Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002-5000

Alicia Dickenstein
Affiliation: Departamento de Matemática, F.C.E. y N., Universidad de Buenos Aires, Cuidad Universitaria–Pabellón I, 1428 Buenos Aires, Argentina

Keywords: Toric variety
Received by editor(s): November 10, 2003
Received by editor(s) in revised form: June 14, 2004
Published electronically: May 2, 2005
Additional Notes: The first author thanks the Mathematics Department of the University of Buenos Aires for their hospitality during his visits there in 2001 and 2003.
The second author was supported by ANPCYT 03-06568, UBACYT X-052 and Conicet, Argentina.
Communicated by: Michael Stillman
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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