Vol. 11, No. 10, 2017

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
A subspace theorem for subvarieties

Min Ru and Julie Tzu-Yueh Wang

Vol. 11 (2017), No. 10, 2323–2337
Abstract

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