Abstract
AbstractLet C be a smooth curve of genus g. For each positive integer r the birational r-gonality s
Highlights
Let C be a smooth curve of genus g
To prove Theorem 1 for the integer r we will use as C the normalization of a nodal curve Y ∈ |OFe(ah + eaf )|, where e := r − 1
Fix an integer z ≤ ae such that there is a spanned L ∈ Picz(C) such that the morphism v : C → Pk, k := h0(C, L) − 1, induced by |L| is birational onto its image
Summary
Let C be a smooth curve of genus g. To prove Theorem 1 for the integer r we will use as C the normalization of a nodal curve Y ∈ |OFe(ah + eaf )|, where e := r − 1. Since OFe(ah + aef ) is spanned, Bertini’s theorem gives that a general Y ∈ |OFe(ah + aef )| is smooth.
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