Polarized surfaces of -genus

Authors:
Maria Lucia Fania and Elvira Laura Livorni

Journal:
Trans. Amer. Math. Soc. **328** (1991), 445-463

MSC:
Primary 14C20; Secondary 14D20, 14J25

MathSciNet review:
992607

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Abstract: Let be a smooth, complex, algebraic, projective surface and let be an ample line bundle on it. Let denote the -genus of the pair . The purpose of this paper is to classify such pairs under the assumption that and the complete linear system contains a smooth curve. If and , Fujita has shown that is very ample and . If and , then and those pairs have been studied by Fujita and Beltrametti, Lanteri, and Palleschi. To study the remaining cases we have examined the two possibilities of being nef or not, for . In the cases in which is nef it turned out to be very useful to iterate the adjunction mapping for ample line bundles as it was done by Biancofiore and Livorni in the very ample case. If there are still open cases to solve in which completely different methods are needed.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1991-0992607-7

Keywords:
Surfaces,
-genus,
sectional genus

Article copyright:
© Copyright 1991
American Mathematical Society