Given an irregular variety of general type, we show that if a general fiber of the Albanese morphism of satisfies certain Hodge theoretic conditions, the -th cohomological support locus of generates . We then show that the condition that the -th cohomological support locus of generates can often be applied to prove the birationality of certain pluricanonical maps of .
Étant donné une variété irrégulière de type général, nous montrons que si une fibre générale du morphisme d’Albanese de satisfait certaines conditions de la théorie de Hodge, le lieu engendre . Nous montrons ensuite que la condition que engendre peut souvent être appliquée pour prouver la birationalité de certaines applications pluricanoniques de .
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Keywords: Cohomological support loci, Pluricanonical maps, Generic vanishing.
Mot clés : Lieux de support cohomologiques, applications pluricanoniques, annulation générique.
Jiang, Zhi 1
@unpublished{AIF_0__0_0_A105_0, author = {Jiang, Zhi}, title = {Cohomological support loci and {Pluricanonical} systems on irregular varieties}, journal = {Annales de l'Institut Fourier}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, year = {2024}, doi = {10.5802/aif.3649}, language = {en}, note = {Online first}, }
Jiang, Zhi. Cohomological support loci and Pluricanonical systems on irregular varieties. Annales de l'Institut Fourier, Online first, 19 p.
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