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Successive minima of projective toric varieties | | Martin Sombra
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16 Sep 2002 | | Subject: | Number Theory; Algebraic Geometry MSC-class: Primary: 11G50; Secondary: 14G40, 14M25 | math.NT math.AG | | Abstract: | We compute the successive minima of the projective toric variety $X_cA$ associated to a finite set $ cA subset ^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 $X_cA$ and of the $cA$-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. | | Source: | arXiv, math.NT/0209195 | | Services: | Forum | Review | PDF | Favorites | |
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