We show that for all n >= 3 and all primes p there are infinitely many simplicial toric varieties of codimension n in the 2n-dimensional affine space whose minimum number of defining equations is equal to n in characteristic p, and lies between 2n - 2 and 2n in all other characteristics. In particular, these are new examples of varieties which are set-theoretic complete intersections only in one positive characteristic. Moreover, we show that the minimum number of binomial equations which define these varieties in all characteristics is 4 for n = 3 and 2n - 2 + ((n-2)(2) ) whenever n >= 4.
On a special class of simplicial toric varieties
BARILE, Margherita
2007-01-01
Abstract
We show that for all n >= 3 and all primes p there are infinitely many simplicial toric varieties of codimension n in the 2n-dimensional affine space whose minimum number of defining equations is equal to n in characteristic p, and lies between 2n - 2 and 2n in all other characteristics. In particular, these are new examples of varieties which are set-theoretic complete intersections only in one positive characteristic. Moreover, we show that the minimum number of binomial equations which define these varieties in all characteristics is 4 for n = 3 and 2n - 2 + ((n-2)(2) ) whenever n >= 4.File in questo prodotto:
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