an:00097891
Zbl 0770.30038
Komeda, Jiryo
On the existence of Weierstrass points whose first non-gaps are five
EN
Manuscr. Math. 76, No. 2, 193-211 (1992).
00009581
1992
j
30F10 14H55
Weierstrass points; algebraic curve; gaps
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.
C.Maclachlan (Aberdeen)
Zbl 0498.30053