Rational approximations on toric varieties

Fuente: arXiv
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Main Author: Huang, Zhizhong
Format: Preprint
Published: 2018
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_version_ 1866908477191880704
author Huang, Zhizhong
author_facet Huang, Zhizhong
contents 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-Roth's work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves correspond, according to Batyrev's terminology, to the centred primitive collections of the fan.
format Preprint
id arxiv_https___arxiv_org_abs_1809_02001
institution arXiv
publishDate 2018
record_format arxiv
spellingShingle Rational approximations on toric varieties
Huang, Zhizhong
Number Theory
Algebraic Geometry
14G05, 14M25
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-Roth's work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves correspond, according to Batyrev's terminology, to the centred primitive collections of the fan.
title Rational approximations on toric varieties
topic Number Theory
Algebraic Geometry
14G05, 14M25
url https://arxiv.org/abs/1809.02001