A note on non-vanishing and applications
| dc.creator | Andreatta, Marco | |
| dc.creator | Wiśniewski, Jarosław A. | |
| dc.date | 1993-02-01 | |
| dc.date.accessioned | 2026-07-07T09:05:47Z | |
| dc.date.available | 2026-07-07T09:05:47Z | |
| dc.description | 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 $ϕ: X\to Y$ is a morphism supported by $K_X+rL$ for some positive rational number $r$. In the present paper we study the evaluation $ϕ^*ϕ_*(L)\to L$ 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 $ϕ$ 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 $ϕ$ for a smooth $X$. | |
| dc.description | 17 pages, Plain Tex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9302001 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9302001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149795 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A note on non-vanishing and applications | |
| dc.type | text |