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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Projectively normal adjunction surfaces


Authors: Marco Andreatta and Edoardo Ballico
Journal: Proc. Amer. Math. Soc. 112 (1991), 919-924
MSC: Primary 14J25
MathSciNet review: 1057947
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Abstract: On a projective surface $ S$ polarized by a very ample line bundle $ L$ one can consider the adjoint bundles $ {({K_S} \otimes L)^{ \otimes n}} = {L^{ \otimes n}}$ and the adjunction mappings associated to them. Suppose these mappings are embeddings (it is well known when this is the case: see [So-VdV]). We prove that these embeddings are projectively normal for $ n \geq 2$ and we describe some counterexamples for $ n = 1$. For $ n \geq 2$ we show that the ideals of the image of $ S$ are generated by quadrics.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1057947-X
PII: S 0002-9939(1991)1057947-X
Keywords: Adjoint bundle, adjunction mapping, projective normality
Article copyright: © Copyright 1991 American Mathematical Society