Abstract.
This note studies the structure of the divisorial fixed part of \(\mid\omega_D\mid\) for a 1-connected curve D on a smooth surface S. It is shown that if the divisorial fixed part F of \(\mid\omega_D\mid\) 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 \(\mid\omega_D\mid\), is also described.
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The second named author is a member of the Center for Mathematical Analysis, Geometry and Dynamical Systems (IST-UTL). This work was partially supported by the Fundação para a Ciência e a Tecnologia through Program POCI 2010/FEDER and Grants-in-Aid for Scientific Research (B) (No. 16340008) by Japan Society for the Promotion of Science (JSPS).
Received: 16 August 2007
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Konno, K., Lopes, M.M. The base components of the dualizing sheaf of a curve on a surface. Arch. Math. 90, 395–400 (2008). https://doi.org/10.1007/s00013-007-2555-y
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DOI: https://doi.org/10.1007/s00013-007-2555-y