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Cyclic coverings of an elliptic curve with two branch points and the gap sequences at the ramification points. (English) Zbl 0938.14012
Here the author constructs a cyclic covering \(\pi:X\to E\) with \(X\) a smooth curve of genus \(g\geq 7\), \(E\) an elliptic curve, \(\pi\) a cyclic covering ramified at exactly two points, say \(P\) and \(Q\), which are totally ramified and such that (seeing them as Weierstrass points on \(X)\) their gap sequence is \(\{1,\dots,g-2,g,2g-1\}\) (characteristic 0).
Reviewer: E.Ballico (Povo)
MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
14H52 Elliptic curves
11G05 Elliptic curves over global fields
14H30 Coverings of curves, fundamental group
14E20 Coverings in algebraic geometry
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