Pluriadjoint bundles of polarized surfaces |
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Authors: | Antonio Lanteri |
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Institution: | (1) Dipartimento di Matematica F. Enriques Università, Via C. Saldini, 50, I-20133 Milano, Italy |
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Abstract: | LetX be a complex connected projective smooth algebraic surface and letL be an ample line bundle onX. The maps associated with the pluriadjoint bundles (K
X
L) 1,t2, are studied by combining an ampleness result forK
X
L with a very recent result by Reider. It turns out that apart from some exceptions and up to reductions, 1) (K
X
L)3 is very ample; 2) (K
X
L) 2 is ample and spanned by global sections and is very ample unless eitherg (L)=2 (arithmetic genus ofL) orX contains an elliptic curveE withE
2=0,E·L=1;3) when (K
X
L) 2 is not very ample, the associated map has degree 4, equality implying thatg (L)=2 and
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Keywords: | |
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