Access the full text.
Sign up today, get DeepDyve free for 14 days.
Kenneth Ascher, A. Turchet (2020)
Hyperbolicity of Varieties of Log General TypeCRM Short Courses
H. Pasten (2017)
Definability of Frobenius orbits and a result on rational distance setsMonatshefte für Mathematik, 182
J. Solymosi, Frank Zeeuw (2008)
On a Question of Erdős and UlamDiscrete & Computational Geometry, 43
Kenneth Ascher, Kristin Devleming, A. Turchet (2018)
Uniformity for integral points on surfaces, positivity of log cotangent sheaves and hyperbolicity
G. Faltings (1983)
Endlichkeitssätze für abelsche Varietäten über ZahlkörpernInventiones mathematicae, 73
Kenneth Ascher, Kristin Devleming, A. Turchet (2018)
Hyperbolicity and Uniformity of Varieties of Log General typeInternational Mathematics Research Notices
Tobias Kreisel, Sascha Kurz (2008)
There Are Integral Heptagons, no Three Points on a Line, no Four on a CircleDiscrete & Computational Geometry, 39
L. Caporaso, J. Harris, B. Mazur (1997)
Uniformity of rational pointsJournal of the American Mathematical Society, 10
(1945)
Integral distances
B. Hassett (1995)
Correlation for surfaces of general typeDuke Mathematical Journal, 85
Sandor Kovacs (2018)
SHORT PROOF OF TERRY TAO’S THEOREM 4 REGARDING BOMBIERI-LANG IMPLIES ERDŐS-ULAM
Shigeetj Iitaka (2010)
Birational Geometry of Algebraic Varieties
G. Faltings (1991)
Diophantine approximation on abelian varietiesAnnals of Mathematics, 133
(2020)
Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli SpacesCRM Short Courses
Alexander Rovira, Nicolas Müller, Weiwen Deng, Chudi Ndubaku, Richmond Sarpong (2019)
Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572cChemical Science, 10
Mehdi Makhul, J. Shaffaf (2012)
On uniform boundedness of a rational distance set in the planeComptes Rendus Mathematique, 350
D. Abramovich (1995)
Uniformity of stably integral points on elliptic curvesInventiones mathematicae, 127
J. Shaffaf (2014)
A Solution of the Erdős–Ulam Problem on Rational Distance Sets Assuming the Bombieri–Lang ConjectureDiscrete & Computational Geometry, 60
J. Kollár, S. Mori (1998)
Birational Geometry of Algebraic Varieties: Index
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.
Bulletin of the London Mathematical Society – Wiley
Published: Dec 1, 2020
Keywords: ; ; ;
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.