On the second adjunction mapping.
The case of a 1-dimensional image
Authors: Mauro C. Beltrametti and Andrew J. Sommese
Journal: Trans. Amer. Math. Soc. 349 (1997), 3277-3302
MSC (1991): Primary 14E35, 14C20, 14J40
MathSciNet review: 1401513
Abstract: Let be a very ample line bundle on an -dimensional projective manifold , i.e., assume that for some embedding . In this article, a study is made of the meromorphic map, , associated to in the case when the Kodaira dimension of is , and has a -dimensional image. Assume for simplicity that . The first main result of the paper shows that is a morphism if either or . The second main result of this paper shows that if , then the genus, , of a fiber, , of the map induced by on hyperplane sections is . Moreover, if then , a connected component of a general fiber of is either a surface or the blowing up at one point of a surface, and . Finally the structure of the finite to one part of the Remmert-Stein factorization of is worked out.
Mauro C. Beltrametti
Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, I-16146 Genova, Italy
Andrew J. Sommese
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Received by editor(s): January 11, 1996
Article copyright: © Copyright 1997 American Mathematical Society