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Mathematische Annalen

, Volume 342, Issue 2, pp 449–466 | Cite as

Intersecting subvarieties of \({G_m^n}\) with algebraic subgroups

  • P. HabeggerEmail author
Article

Abstract

Let \({X\subset G_m^n}\) be an irreducible closed subvariety defined over \({\bar{Q}}\). We bound the height of algebraic points on X that are in a certain sense close to the union of all algebraic subgroup of \({G_m^n}\) of dimension m < n/dim X. The bound we obtain is effective and will be expressed as a function of the height of X, the degree of X, and n. We then apply this bound to derive certain finiteness results if m is also strictly less than n − dim X.

Mathematics Subject Classification (2000)

11G50 14G25 14G40 14J20 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departement MathematikETH ZürichZurichSwitzerland

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