Pluricanonical maps of varieties of maximal Albanese dimension

dc.creatorChen, Jungkai A.
dc.creatorHacon, Christopher D.
dc.date2000-05-19
dc.date2000-05-20
dc.date.accessioned2026-07-07T04:35:22Z
dc.date.available2026-07-07T04:35:22Z
dc.descriptionLet $X$ 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.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0005187
dc.identifierhttp://arxiv.org/abs/math/0005187
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59232
dc.subjectAlgebraic Geometry
dc.subject14C20; 14F17
dc.titlePluricanonical maps of varieties of maximal Albanese dimension
dc.typetext

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