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On the iteration of the adjunction process for surfaces of negative Kodaira dimension

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Abstract

Let (X,L) be a pair consisting of a smooth, complex, projective surface X and L a very ample line bundle on it. Suppose that the Kodaira dimension K(X) of X is negative. Then using the results obtained by A.J.Sommese and A.Van de Ven in [11], we find that the sectional genus, gk=g(Lk), of the successive iterated minimal reductions (Xk,Lk), see 1. for the definition, reach a maximum value and then monotonically decrease to a final value gn=g(Ln)≤g=g(L). This result gives a concrete way to express any pair (X,L), with K(X)=−∞, in terms of a minimal model.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Via Roma, Pal.Del Tosto, 67100, L'Aquila, Italy

    Aldo Biancofiore-Elvira & Laura Livorni

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  1. Aldo Biancofiore-Elvira
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  2. Laura Livorni
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Biancofiore-Elvira, A., Livorni, L. On the iteration of the adjunction process for surfaces of negative Kodaira dimension. Manuscripta Math 64, 35–54 (1989). https://doi.org/10.1007/BF01182084

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  • DOI: https://doi.org/10.1007/BF01182084

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