Bounding heights uniformly in families of hyperbolic varieties

Kenneth Ascher; Ariyan Javanpeykar

Bounding heights uniformly in families of hyperbolic varieties

Kenneth Ascher, Ariyan Javanpeykar

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show, assuming Vojta’s height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded “uniformly” in families. This generalizes a result of Su-Ion Ih for curves of genus at least two to higher-dimensional varieties. As an application, we show that, assuming Vojta’s height conjecture, the height of a rational point on a curve of general type is uniformly bounded. Finally, we prove a similar result for smooth hyperbolic surfaces with c²₁ < c₂.

Original language	English (US)
Pages (from-to)	1791-1808
Number of pages	18
Journal	New York Journal of Mathematics
Volume	23
State	Published - Dec 11 2017

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

General type
Heights
Hyperbolicity
Moduli spaces
Rational points
Vojta’s conjecture

Cite this

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AB - We show, assuming Vojta’s height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded “uniformly” in families. This generalizes a result of Su-Ion Ih for curves of genus at least two to higher-dimensional varieties. As an application, we show that, assuming Vojta’s height conjecture, the height of a rational point on a curve of general type is uniformly bounded. Finally, we prove a similar result for smooth hyperbolic surfaces with c21 < c2.

KW - General type

KW - Heights

KW - Hyperbolicity

KW - Moduli spaces

KW - Rational points

KW - Vojta’s conjecture

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JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Bounding heights uniformly in families of hyperbolic varieties

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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