A subspace theorem for subvarieties. (English) Zbl 1439.11181

Ru, Min; Wang, Julie

Algebra Number Theory 11, No. 10, 2323-2337 (2017).

Summary: 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 D. McKinnon and M. Roth [Invent. Math. 200, No. 2, 513–583 (2015; Zbl 1337.14023)]. The inequality obtained in this paper connects the result of McKinnon and Roth (the case when the subschemes are points) and the results of P. Corvaja and U. Zannier [Am. J. Math. 126, No. 5, 1033–1055 (2004; Zbl 1125.11022)], J.-H. Evertse and R. G. Ferretti [Int. Math. Res. Not. 2002, No. 25, 1295–1330 (2002; Zbl 1073.14521)], the author [Funct. Approximatio, Comment. Math. 56, No. 2, 143–163 (2017; Zbl 1432.11101)], and the author and P. Vojta [“A birational Nevanlinna constant and its consequences”, Preprint, arXiv:1608.05382] (the case when the subschemes are divisors). Furthermore, our approach gives an alternative short and simpler proof of McKinnon and Roth’s result.

MSC:

11J97	Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.)
11J87	Schmidt Subspace Theorem and applications
14G05	Rational points

Keywords:

Schmidt’s subspace theorem; Roth’s theorem; Diophantine approximation; Vojta’s conjecture

Citations:

Zbl 1337.14023; Zbl 1125.11022; Zbl 1073.14521; Zbl 1432.11101

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