an:05230405
Zbl 1143.14026
Kang, Eunju; Kim, Seon Jeong
A Weierstrass semigroup at a pair of inflection points on a smooth plane curve
EN
Bull. Korean Math. Soc. 44, No. 2, 369-378 (2007).
00208558
2007
j
14H55 14H51 14H45 14G50
Weierstrass semigroup; plane curve, inflection points
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 \textit{S. J. Kim} [Arch. Math. (Basel) 62, No. 1, 73--82 (1994; Zbl 0815.14020)] and \textit{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 \textit{M. Coppens} and \textit{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.
Jos?? Gilvan de Oliveira (Vit??ria)
Zbl 0815.14020; Zbl 0869.14015; Zbl 0910.14013