Advanced Studies in Pure Mathematics

Some geometric-arithmetic aspects of separated variable curves

Viet Khac Nguyen

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The paper shows certain geometric-arithmetic aspects with some new observations in consideration of variables separated curves, e.g. relationships with generalized Chebyshev polynomials, Chebyshev pencils, local variant at infinity of Stothers–Mason $abc$-theorem, Stothers–Langevin pairs, Pell–Abel conics (or polynomial Pell equations), Belyi maps, etc. Several case studies and open problems are discussed.

Article information

Source
Singularities in Geometry and Topology 2011, V. Blanlœil and O. Saeki, eds. (Tokyo: Mathematical Society of Japan, 2015), 161-172

Dates
Received: 22 March 2012
Revised: 30 July 2012
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916286

Digital Object Identifier
doi:10.2969/aspm/06610161

Mathematical Reviews number (MathSciNet)
MR3382049

Zentralblatt MATH identifier
1360.11076

Subjects
Primary: 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25] 14H10: Families, moduli (algebraic)

Keywords
Chebyshev polynomial Stothers–Mason abc-theorem Stothers–Langevin pair Pell–Abel conics

Citation

Nguyen, Viet Khac. Some geometric-arithmetic aspects of separated variable curves. Singularities in Geometry and Topology 2011, 161--172, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06610161. https://projecteuclid.org/euclid.aspm/1539916286


Export citation