Bounding heights uniformly in families of hyperbolic varieties

Kenneth Ascher, Ariyan Javanpeykar

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1791-1808
Number of pages18
JournalNew York Journal of Mathematics
Volume23
StatePublished - Dec 11 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

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