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

Mathematics – Algebraic Geometry

Scientific paper

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7pp., to appear in Archive der Mathematik

Scientific paper

This note studies the structure of the divisorial fixed part of the dualizing
sheaf of a 1-connected curve D on a smooth surface S. It is shown that if the
divisorial fixed part F of the dualizing sheaf is non empty then it has
arithmetic genus<1 and each component of F is a smooth rational curve.

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