The canonical ring of a 3-connected curve

2011/07/27 by Marco Franciosi, Franciosi, Marco, Elisa Tenni +1
Mathematics · #14C20 #14H20 #14H51 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C20 #msc:14H20 #msc:14H51

paper · pdf · doi:10.48550/arxiv.1107.5535

arxiv created 2013/04/23 · arxiv updated 2013/04/24

Abstract

Let C be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. We show that the canonical ring R(C, ω_C)= ⊕_{k ≥ 0} H⁰(C, ω_C^k is generated in degree 1 if C is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C, L)=⊕_{k ≥ 0} H⁰(C,L^k) is generated in degree 1 if C is reduced with planar singularities and L is an invertible sheaf such that deg L_|B ≥ 2p_a(B)+1 for every B ⊆ C.

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