Approximating rational points on toric varieties
Authors:
David McKinnon and Matthew Satriano
Journal:
Trans. Amer. Math. Soc. 374 (2021), 3557-3577
MSC (2020):
Primary 14G05; Secondary 11G50, 11J97
DOI:
https://doi.org/10.1090/tran/8318
Published electronically:
February 8, 2021
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a smooth projective variety over a number field
and
, the first author conjectured that in a precise sense, any sequence that approximates
sufficiently well must lie on a rational curve. We prove this conjecture for smooth split toric surfaces conditional on Vojta's conjecture. More generally, we show that if
is a
-factorial terminal split toric variety of arbitrary dimension, then
is better approximated by points on a rational curve than by any Zariski dense sequence.
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Additional Information
David McKinnon
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Email:
dmckinnon@uwaterloo.ca
Matthew Satriano
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Email:
msatrian@uwaterloo.ca
DOI:
https://doi.org/10.1090/tran/8318
Received by editor(s):
May 19, 2020
Received by editor(s) in revised form:
September 15, 2020
Published electronically:
February 8, 2021
Additional Notes:
The authors were partially supported by Discovery Grants from the Natural Sciences and Engineering Research Council
Article copyright:
© Copyright 2021
American Mathematical Society