Vol. 11, No. 10, 2017

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A subspace theorem for subvarieties

Min Ru and Julie Tzu-Yueh Wang

Vol. 11 (2017), No. 10, 2323–2337

We establish a height inequality, in terms of an (ample) line bundle, for a sum of subschemes located in -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.

Schmidt's subspace theorem, Roth's theorem, Diophantine approximation, Vojta's conjecture
Mathematical Subject Classification 2010
Primary: 11J97
Secondary: 11J87, 14G05
Received: 1 September 2016
Revised: 6 February 2017
Accepted: 31 March 2017
Published: 31 December 2017
Min Ru
Department of Mathematics
East China Normal University
China Department of Mathematics
University of Houston
Houston, TX
United States
Julie Tzu-Yueh Wang
Institute of Mathematics
Academia Sinica