Pluricanonical maps of varieties of maximal Albanese dimension
| dc.creator | Chen, Jungkai A. | |
| dc.creator | Hacon, Christopher D. | |
| dc.date | 2000-05-19 | |
| dc.date | 2000-05-20 | |
| dc.date.accessioned | 2026-07-07T04:35:22Z | |
| dc.date.available | 2026-07-07T04:35:22Z | |
| dc.description | Let $X$ be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of $κ(X)$ in terms of the set $V^0(X,ω_{X})$ $:=\{P\in {\text{\rm Pic}}^0(X)|h^0(X, ω_X \otimes P) \ne 0\}$. An immediate consequence of this is that the Kodaira dimension $κ(X)$ is invariant under smooth deformations. We then study the pluricanonical maps $ϕ_m:X -> \Bbb{P} (H^0(X,mK_X))$. We prove that if $X$ is of general type, $ϕ_m$ is generically finite for $m\geq 5$ and birational for $m\geq 5 \text{\rm dim} (X) +1$. More generally, we show that for $m\geq 6$ the image of $ϕ_m$ is of dimension equal to $κ(X)$ and for $m\geq 6κ(X)+2$, $ϕ_m$ is the stable canonical map. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0005187 | |
| dc.identifier | http://arxiv.org/abs/math/0005187 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59232 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C20; 14F17 | |
| dc.title | Pluricanonical maps of varieties of maximal Albanese dimension | |
| dc.type | text |