Local positivity and effective Diophantine approximation

In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity of divisors combined with Faltings’s version of Siegel’s lemma instead of a zero estimate such as Dyson’s lemma. We then use it to prove an effective t...

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Bibliographic Details
Published in:	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Vol. 92; no. 2; pp. 125 - 138
Main Author:	Nickel, Matthias
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2022 Springer Nature B.V
Subjects:	Algebra Approximation Differential Geometry Geometry Mathematical analysis Mathematics Mathematics and Statistics Number Theory Topology Diophantine approxmiation 11J68 14C20 Positivity of divisors Seshadri constants
Online Access:	Get full text
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Summary:	In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity of divisors combined with Faltings’s version of Siegel’s lemma instead of a zero estimate such as Dyson’s lemma. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with complex coefficients.
ISSN:	0025-5858 1865-8784
DOI:	10.1007/s12188-022-00260-8