Let Sigma C PN be a smooth connected arithmetically Cohen-Macaulay surface. Then there are at most finitely many complete linear systems on Sigma, not of the type |kH - K| (H hyperplane section and K canonical divisor on Sigma), containing arithmetically Gorenstein curves.
@article{urn:eudml:doc:42943, title = {Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.}, journal = {Collectanea Mathematica}, volume = {53}, year = {2002}, pages = {265-276}, zbl = {1026.14013}, mrnumber = {MR1940328}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42943} }
Dolcetti, Alberto. Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.. Collectanea Mathematica, Tome 53 (2002) pp. 265-276. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42943/