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Double covers of plane curves of degree six with almost total flexes. (English) Zbl 1427.14065
Let $$f: X\to C$$ be a double covering of smooth projective curves. Let $$P\in C$$ be a ramification point of $$f$$ with $$f(P')=P$$. Let $$H(P)$$ and $$H(P')$$ be the Weierstrass semigroup of $$P$$ and $$P'$$, respectively. The authors pose the problem of the clasification of all $$H(P')$$ for all smooth plane curves. They solved it here when $$C$$ has degree $$6$$. They did the case $$\deg (C)=5$$ in [S. J. Kim and J. Komeda, Kodai Math. J. 38, No. 2, 270–288 (2015; Zbl 1327.14159)] and did some other cases in [S. J. Kim and J. Komeda, Bull. Korean Math. Soc. 55, No. 2, 611–624 (2018; Zbl 1401.14158)].
##### MSC:
 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H50 Plane and space curves 14H30 Coverings of curves, fundamental group 20M14 Commutative semigroups
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##### References:
 [1] T. Harui and J. Komeda, Numerical semigroups of genus eight and double coverings of curves of genus three, Semigroup Forum 89 (2014), no. 3, 571-581. https://doi.org/ 10.1007/s00233-014-9590-3 · Zbl 1309.14026 [2] S. J. Kim and J. Komeda, Weierstrass semigroups on double covers of genus 4 curves, J. Algebra 405 (2014), 142-167. https://doi.org/10.1016/j.jalgebra.2014.02.006 · Zbl 1395.14028 [3] , Weierstrass semigroups on double covers of plane curves of degree 5, Kodai Math. J. 38 (2015), no. 2, 270-288. https://doi.org/10.2996/kmj/1436403890 · Zbl 1327.14159 [4] , Weierstrass semigroups on double covers of plane curves of degree six with total flexes, Bull. Korean Math. Soc. 55 (2018), no. 2, 611-624. · Zbl 1401.14158
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