Rational approximations on toric varieties

authored by

Zhizhong Huang

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Algebra and Number Theory

Volume

15

Pages

461-512

No. of pages

52

ISSN

1937-0652

Publication date

07.04.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://arxiv.org/abs/1809.02001 (Access: Open)
https://doi.org/10.2140/ant.2021.15.461 (Access: Closed)