Kim, Seon Jeong; Komeda, Jiryo The Weierstrass semigroups on the quotient curve of a plane curve of degree \(\leqslant 7\) by an involution. (English) Zbl 1171.14020 J. Algebra 322, No. 1, 137-152 (2009). Summary: First we describe the Weierstrass semigroups on a plane curve of degree \(\leqslant 6\). Using this description we determine the Weierstrass semigroups at a ramification point and a branch point on a double covering from a plane curve of degree \(\leqslant 6\). In the case of a double covering from a plane curve of degree 7 we determine all the Weierstrass semigroups at branch points. Cited in 2 ReviewsCited in 1 Document MSC: 14H51 Special divisors on curves (gonality, Brill-Noether theory) Keywords:Weierstrass point; Weierstrass semigroup; smooth plane curve; double covering of a curve PDF BibTeX XML Cite \textit{S. J. Kim} and \textit{J. Komeda}, J. Algebra 322, No. 1, 137--152 (2009; Zbl 1171.14020) Full Text: DOI References: [1] Coppens, M., The existence of base point free linear systems on smooth plane curves, J. algebraic geom., 4, 1-15, (1995) · Zbl 0842.14020 [2] Coppens, M.; Kato, T., The Weierstrass gap sequences at an inflection point on a nodal plane curve, aligned inflection points on plane curves, Boll. unione mat. ital. sez. B (7), 11, 1-33, (1997) · Zbl 0910.14013 [3] Kikuchi, S., Bound for the Weierstrass weights of points on a smooth plane algebraic curve, Tsukuba J. math., 27, 359-374, (2003) · Zbl 1077.14042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.