JournalsrlmVol. 25, No. 1pp. 37–51

The canonical ring of a 3-connected curve

  • Marco Franciosi

    Università di Pisa, Italy
  • Elisa Tenni

    Università di Firenze, Italy
The canonical ring of a 3-connected curve cover
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Abstract

Let CC be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. We show that the canonical ring R(C,ωC)=k0H0(C,ωCk)R(C, \omega_C) = \bigoplus_{k\geq 0} H^0(C, {\omega_C}^{\otimes k}) is generated in degree 1 if CC is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C,L)=k0H0(C,Lk)R(C, L)=\bigoplus_{k\geq 0} H^0(C,L^{\otimes k}) is generated in degree 1 if CC is reduced with planar singularities and LL is an invertible sheaf such that degLB2pa(B)+1\deg L_{|B} \geq 2p_a(B)+1 for every BCB\subseteq C.

Cite this article

Marco Franciosi, Elisa Tenni, The canonical ring of a 3-connected curve. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 1, pp. 37–51

DOI 10.4171/RLM/667