Cohomological support loci and Pluricanonical systems on irregular varieties
[Lieux de support cohomologiques et systèmes pluricanoniques sur des variétés irrégulières]
Jiang, Zhi1
1 Shanghai Center for Mathematical Sciences, Fudan University, Songhu Road 2005, Shanghai (China)
Annales de l'Institut Fourier, Online first, 19 p.

Étant donné une variété irrégulière X de type général, nous montrons que si une fibre générale du morphisme d’Albanese de X satisfait certaines conditions de la théorie de Hodge, le lieu V 0 (K X ) engendre Pic 0 (X). Nous montrons ensuite que la condition que V 0 (K X ) engendre Pic 0 (X) peut souvent être appliquée pour prouver la birationalité de certaines applications pluricanoniques de X.

Given an irregular variety X of general type, we show that if a general fiber F of the Albanese morphism of X satisfies certain Hodge theoretic conditions, the 0-th cohomological support locus of K X generates Pic 0 (X). We then show that the condition that the 0-th cohomological support locus of K X generates Pic 0 (X) can often be applied to prove the birationality of certain pluricanonical maps of X.

Reçu le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3649
Classification : 14E05, 14D07, 14F10
Keywords: Cohomological support loci, Pluricanonical maps, Generic vanishing.
Mot clés : Lieux de support cohomologiques, applications pluricanoniques, annulation générique.
Jiang, Zhi 1

1 Shanghai Center for Mathematical Sciences, Fudan University, Songhu Road 2005, Shanghai (China) 
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Jiang, Zhi. Cohomological support loci and Pluricanonical systems on irregular varieties. Annales de l'Institut Fourier, Online first, 19 p.

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