Following the ideas of Castelnuovo and Enriques, we classify the birational equivalence classes of double planes which are rational or ruled surfaces. In order to do this, we prove that the vanishing of the m-adjoint linear system to the branch curve of the canonical resolution of a double plane, for m ≥ 2, is a necessary and sufficient condition for the ruledness of the double plane.
On rational and ruled double planes
CALABRI, Alberto
2002
Abstract
Following the ideas of Castelnuovo and Enriques, we classify the birational equivalence classes of double planes which are rational or ruled surfaces. In order to do this, we prove that the vanishing of the m-adjoint linear system to the branch curve of the canonical resolution of a double plane, for m ≥ 2, is a necessary and sufficient condition for the ruledness of the double plane.File in questo prodotto:
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2002_AnnaliMatematicaPuraApplicata_myc8l18tuh1lxwey_On rational and ruled double planes.pdf
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