Pluricanonical maps of varieties of maximal Albanese dimension
By Jungkai A. Chen, Christopher D. Hacon. 2000
54 citations recorded by the source corpus.
Abstract. Let X be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of $\kappa (X)$ in terms of the set $V^0(X,\omega_{X} ):=\{ P\in{\mbox{\rm Pic}}^0(X)|h^0(X, \omega_X \otimes P) \ne 0\}$. An immediate consequence of this is that the Kodaira dimension $\kappa (X)$ is invariant under smooth deformations. We then study the pluricanonical maps $\varphi _m:X \dashrightarrow \mathbb{P} (H^0(X,mK_X))$. We prove that if X is of general type, $\varphi _m$ is generically finite for $m\geq 5$ and birational for $m\geq 5 \mbox{\rm dim} (X) +1$. More generally, we show that for $m\geq 6$ the image of $\varphi _m$ is of dimension equal to $\kappa (X)$ and for $m\geq 6\kappa (X)+2$, $\varphi _m$ is the stable canonical map.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6704a47b7a804c9cf1acb430aae3c48643ba2b37
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On pluricanonical systems of algebraic varieties of general type (2008, result): “When q(V ) > 0, λ(V ) ≤ 3 by Chen-Hacon [4].”