Representations of divisors on hyperelliptic curves, Gröbner bases and plane curves with quasi-toric relations

Abstract

In the study of hyperelliptic curve cryptography, presentations of semi-reduced divisors on a hyperelliptic curve play important roles. In this note, we give an interpretation for such presentations from view points of Gröbner bases. As applications, (i) we give a method to construct weak $n$-contact curves and (ii) we study plane curves satisfying quasi-toric relations of type $(2,n,2)$

13 pages

References in corpus (1)

• Mordell-Weil groups of elliptic threefolds and the Alexander module of plane curves

Cited by in corpus (1)

• The geometry of three sections on certain rational elliptic surfaces and Mumford representations