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Trigonal Gorenstein curves. (English) Zbl 1059.14038
Summary: We notice that the Maroni invariant of a trigonal Gorenstein curve of arithmetic genus \(g\) larger than four may be equal to zero, and we show that this happens if and only if the \(g^1_3\) admits a non-removable base point, which is necessarily a singularity of the curve. We realize and study trigonal curves on rational scrolls, which in the case, where the \(g^1_3\) admits a base point \(Q\), degenerate to a cone with vertex \(Q\).

MSC:
14H51 Special divisors on curves (gonality, Brill-Noether theory)
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