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Gonality of non-Gorenstein curves of genus five. (English) Zbl 1308.14029
Summary: We establish sufficient conditions for some curves to be trigonal and derive from them that most of non-Gorenstein curves of genus five are so. Afterwards, we show that the gonality of such a curve ranges from 2 to 5. Gonality is understood within a broader context, i.e., the \(g_{d}^{1}\) may possibly admit a base point and correspond to a torsion free sheaf of rank one instead of a line bundle. This study comes along with a thorough description of possible canonical models and kinds of singularities.

MSC:
14H20 Singularities of curves, local rings
14H45 Special algebraic curves and curves of low genus
14H51 Special divisors on curves (gonality, Brill-Noether theory)
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