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HIGHER ORDER EMBEDDINGS OF CERTAIN BLOW-UPS OFℙ²

CINDY DE VOLDER and HALSZKA TUTAJ-GASIŃSKA
Proceedings of the American Mathematical Society
Vol. 137, No. 12 (DECEMBER 2009), pp. 4089-4097
Stable URL: http://www.jstor.org/stable/40590645
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
HIGHER ORDER EMBEDDINGS OF CERTAIN BLOW-UPS OFℙ²
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Abstract

Let X n be the blow-up of the projective plane along n general points of a smooth cubic plane curve and let be the linear series of strict transforms of plane curves of degree d having multiplicity at least m i at the i-th blown-up point. We prove that if is L is κ-very ample, then L is excellent and L· (– K n ) ≥+ 2. Then we give a numerical criterion for the k-very ampleness of excellent classes with L· (– K n ) ≥ k + 2, which in many cases is a necessary and sufficient condition.

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