A Weierstrass semigroup at a pair of inflection points on a smooth plane curve. (English) Zbl 1143.14026

Kang, Eunju; Kim, Seon Jeong

Bull. Korean Math. Soc. 44, No. 2, 369-378 (2007).

Let \(C\) be a smooth complex projective plane curve of degree \(d\geq 4\). The authors use some results about Weierstrass semigroup at a pair of points, due to S. J. Kim [Arch. Math. (Basel) 62, No. 1, 73–82 (1994; Zbl 0815.14020)] and M. Homma [Arch. Math. (Basel) 67, No. 4, 337–348 (1996; Zbl 0869.14015)], to describe all six possible Weierstrass semigroups at a pair of inflection points on \(C\) of multiplicities \(d\) or \(d-1.\) Moreover, by using a result due to M. Coppens and T. Kato [Boll. Un. Mat. Ital. B (7), No. 1, 1–33 (1997; Zbl 0910.14013)], they prove that for each one of them there exist such a curve \(C\) with a pair of inflection points having such semigroup as their Weierstrass semigroup.

Reviewer: José Gilvan de Oliveira (Vitória)

MSC:

14H55	Riemann surfaces; Weierstrass points; gap sequences
14H51	Special divisors on curves (gonality, Brill-Noether theory)
14H45	Special algebraic curves and curves of low genus
14G50	Applications to coding theory and cryptography of arithmetic geometry

Keywords:

Weierstrass semigroup; plane curve, inflection points