The base components of the dualizing sheaf of a curve on a surface

摘要

This note studies the structure of the divisorial fixed part of | w_D |midomega_Dmid for a 1-connected curve D on a smooth surface S. It is shown that if the divisorial fixed part F of | w_D |midomega_Dmid is non empty then it has arithmetic genus ≤ 0 and each component of F is a smooth rational curve. The structure of curves D, with non empty divisorial fixed part F for | w_D |midomega_Dmid, is also described.