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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
##### Keywords:
Weierstrass semigroup; plane curve, inflection points
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