On the geometry of complete intersection toric varieties |
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Authors: | Nickolas J Michelacakis Apostolos Thoma |
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Institution: | (1) Department of Mathematics and Statistics, University of Cyprus, Nicosia, 1678, Cyprus;(2) Department of Mathematics, University of Ioannina, Ioannina, 45110, Greece |
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Abstract: | In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular,
we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and
contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal
to 2n − 2, is exactly 2n − 2 if and only if the cone is a bipyramidal cone, where n > 1 is the dimension of the cone. Finally, we characterize all toric varieties whose associated cones are complete intersection
cones.
Received: 4 July 2005 |
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Keywords: | 14M25 14M10 |
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