Abstract
A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's conjecture, that the cardinalities of rational distance sets in general position are uniformly bounded, generalizing results of Solymosi–de Zeeuw, Makhul–Shaffaf, Shaffaf and Tao. In the process, we give a criterion for certain varieties with non-canonical singularities to be of general type.
Original language | English (US) |
---|---|
Pages (from-to) | 1053-1063 |
Number of pages | 11 |
Journal | Bulletin of the London Mathematical Society |
Volume | 52 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2020 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- 14G05
- 14J17
- 14J29 (secondary)
- 52C10 (primary)