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arXiv · 1509.05898

The number of maximal torsion cosets in subvarieties of tori

César Martínez
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Abstract

We present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus $\mathbb{G}_{\textrm{m}}^n$. Our first main result gives a bound in terms of the degree of the defining polynomials. A second result gives a bound in terms of the toric degree of the subvariety. As a consequence, we prove the conjectures of Ruppert and of Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.

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César Martínez. 2015-09-19. The number of maximal torsion cosets in subvarieties of tori. https://arxiv.org/abs/1509.05898

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