A subspace theorem for subvarieties

Ru, Min; Wang, Julie

doi:10.2140/ant.2017.11.2323

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A subspace theorem for subvarieties

Min Ru and Julie Tzu-Yueh Wang

Vol. 11 (2017), No. 10, 2323–2337

DOI: 10.2140/ant.2017.11.2323

Abstract

We establish a height inequality, in terms of an (ample) line bundle, for a sum of subschemes located in $ℓ$ -subgeneral position in an algebraic variety, which extends a result of McKinnon and Roth (2015). The inequality obtained in this paper connects the result of McKinnon and Roth (the case when the subschemes are points) and the results of Corvaja and Zannier (2004), Evertse and Ferretti (2008), Ru (2017), and Ru and Vojta (2016) (the case when the subschemes are divisors). Furthermore, our approach gives an alternative short and simpler proof of McKinnon and Roth’s result.

Keywords

Schmidt's subspace theorem, Roth's theorem, Diophantine approximation, Vojta's conjecture

Mathematical Subject Classification 2010

Primary: 11J97

Secondary: 11J87, 14G05

Milestones

Received: 1 September 2016

Revised: 6 February 2017

Accepted: 31 March 2017

Published: 31 December 2017

Authors

Min Ru
Department of Mathematics East China Normal University Shanghai China Department of Mathematics University of Houston Houston, TX United States

Julie Tzu-Yueh Wang
Institute of Mathematics Academia Sinica Taipei Taiwan

Vol. 11, No. 10, 2017