Successive minima of projective toric varieties

Martin Sombra

Successive minima of projective toric varieties

Number Theory 2016-09-07 v2 Algebraic Geometry

Authors: Martin Sombra

Abstract

We compute the successive minima of the projective toric variety $X_\cA$ associated to a finite set $\cA \subset \Z^n$ . 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.

Keywords

successive minima projective toric variety height estimates a-resultant arithmetic bezout-kushnirenko theorem sparse nullstellensatz

Cite

@article{arxiv.math/0209195,
  title  = {Successive minima of projective toric varieties},
  author = {Martin Sombra},
  journal= {arXiv preprint arXiv:math/0209195},
  year   = {2016}
}

Comments

Revised version. In French, 25 pp

Successive minima of projective toric varieties

Abstract

Keywords

Cite

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