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2021 Rational approximations on toric varieties
Zhizhong Huang
Algebra Number Theory 15(2): 461-512 (2021). DOI: 10.2140/ant.2021.15.461

Abstract

Using the universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain geometric hypothesis the best approximations (in the sense of McKinnon and Roth’s work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves are also minimal in the sense of deformation theory, and they correspond, according to Batyrev’s terminology, to the centred primitive collections of the structural fan.

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Zhizhong Huang. "Rational approximations on toric varieties." Algebra Number Theory 15 (2) 461 - 512, 2021. https://doi.org/10.2140/ant.2021.15.461

Information

Received: 1 January 2020; Revised: 27 July 2020; Accepted: 24 August 2020; Published: 2021
First available in Project Euclid: 23 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.461

Subjects:
Primary: 14G05
Secondary: 11J99 , 14M25

Keywords: Diophantine approximation of rational points , toric varieties , universal torsors

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 2 • 2021
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