A note on nonvanishing and applications
Abstract
Let $X$ be a normal variety over the field of complex numbers with log terminal singularities and the canonical divisor $K_X$ being ${\bf Q}$Gorenstein. Assume that $L$ is an ample line bundle over $X$ and $\phi: X\to Y$ is a morphism supported by $K_X+rL$ for some positive rational number $r$. In the present paper we study the evaluation $\phi^*\phi_*(L)\to L$ and the locus of points where it is not surjective which we call relative base point locus of $L$. In particular, we prove that, if the dimension of a fiber of $\phi$ is small with respect to $r$ then the relative base point locus does not meet the fiber. Consequently, in this case, we discuss the structure of the map $\phi$ for a smooth $X$.
 Publication:

arXiv eprints
 Pub Date:
 February 1993
 arXiv:
 arXiv:alggeom/9302001
 Bibcode:
 1993alg.geom..2001A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 17 pages, Plain Tex