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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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Keywords: Adjoint bundle, adjunction mapping, projective normality
Article copyright: © Copyright 1991 American Mathematical Society

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