Successive minima of projective toric varieties
Abstract
We compute the successive minima of the projective toric variety X associated to a finite set ⊂ n. As a consequence of this computation and of the results of S.-W. Zhang on the distribution of small points, we derive estimates for the height of the subvariety X and of the -resultant. These estimates allow us to obtain an arithmetic analogue of the Bezout-Kushnirenko's theorem concerning the number of solutions of a system of polynomial equations. As an application of this result, we improve the known estimates for the height of the polynomials in the sparse Nullstellensatz.
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