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On the existence of Weierstrass points whose first non-gaps are five. (English) Zbl 0770.30038
Let \(H\) be a cofinite subsemigroup of the additive semigroup \(\mathbb{N}\), with \(a\), the least member of \(H\). The author shows that, if \(a=5\), there exists a compact Riemann surface \(X\) and a point \(P\) on \(X\), such that \(H\) is the semigroup of non-gaps at \(P\). In an earlier paper [J. Reine Angew. Math. 341, 68-86 (1983; Zbl 0498.30053)] the author had developed algebraic criteria for the existence of curves with prescribed non-gaps. There the related problem for \(a=4\) was solved and here some extensions are given which enable the case \(a=5\) to be solved.

MSC:
30F10 Compact Riemann surfaces and uniformization
14H55 Riemann surfaces; Weierstrass points; gap sequences
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References:
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