Kodaira Dimension of Subvarieties
| dc.creator | Peternell, Thomas | |
| dc.creator | Schneider, Michael | |
| dc.creator | Sommese, Andrew J. | |
| dc.date | 1998-04-07 | |
| dc.date.accessioned | 2026-07-07T05:24:20Z | |
| dc.date.available | 2026-07-07T05:24:20Z | |
| dc.description | In this article we study how the birational geometry of a normal projective variety $X$ is influenced by a normal subvariety $A \subset X.$ One of the most basic examples in this context is provided by the following situation. Let $f:X\to Y$ be a surjective holomorphic map with connected fibers between compact connected complex manifolds. It is well known that given a general fiber $A$ of $f$ we have $$ κ(X)\le κ(A)+\dim Y. $$ This article grew out of the realization that this result should be true with $\dim Y$ replaced by the codimension $\cod_X A$ for a pair $(X,A)$ consisting of a normal subvariety $A$ of a compact normal variety $X$ under weak semipositivity conditions on the normal sheaf of $A$ and the weak singularity condition $\cod_A (A\cap\sing X)\ge 2$. We shall now state our main results in the special case of a submanifold $A$ in a projective manifold $X$ and we also simplify the semipositivity notion. | |
| dc.identifier | https://arxiv.org/abs/math/9804034 | |
| dc.identifier | http://arxiv.org/abs/math/9804034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76799 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Kodaira Dimension of Subvarieties | |
| dc.type | text |