The canonical ring of a 3-connected curve

Details The canonical ring of a 3-connected curve The canonical ring of a 3-connected curve

2011-07-27

arxiv.org/abs/1107.5535v1

Mathematics

Algebraic Geometry

Scientific paper

Let C be a Gorenstein curve which is either reduced or contained in a smooth algebraic surface. We show that the canonical ring R(C, \omega_C)=\oplus_{k \geq 0} H^0(C, \omega_C^k) is generated in degree 1 if C is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C, L)=\oplus_{k \geq 0} H^0(C,L^k) is generated in degree 1 if C is reduced and L is an invertible sheaf such that deg L_{|B} \geq 2p_a(B)+1 for every subcurve B \subset C.

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