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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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[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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