Computing unit groups of curves. (May 2021)

• Record Type: Journal Article
• Authors: Chen, Justin; Vemulapalli, Sameera; Zhang, Leon
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 236
• Page End: 255
• Publication Date: 2021-05
• Subjects: Unit groups -- Divisor classes -- Intrinsic tropicalization -- Tropical geometry; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.05.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The group of units modulo constants of an affine variety over an algebraically closed field is free abelian of finite rank. Computing this group is difficult but of fundamental importance in tropical geometry, where it is necessary in order to realize intrinsic tropicalizations. We present practical algorithms for computing unit groups of smooth curves of low genus. Our approach is rooted in divisor theory, based on interpolation in the case of rational curves and on methods from algebraic number theory in the case of elliptic curves.