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

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
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