Cohomological support loci and Pluricanonical systems on irregular varieties

2021/08/16 by Zhi Jiang, Jiang, Zhi
Mathematics · #14D07 #14E05 #14F10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:14D07 #msc:14E05 #msc:14F10

paper · pdf · doi:10.48550/arxiv.2108.06956

arxiv created 2021/08/16 · openalex publication_date 2021/08/16 · arxiv updated 2021/08/17 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

For 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 condition, the 0-th cohomological support loci of K_X generates the Picard variety of X . We then show that the condition that the 0-th cohomological support loci of K_X generates the Picard variety of X can often be applied to prove the birationality of certain pluricanonical maps of X.

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• Generic Vanishing Index and the Birationality of the Bicanonical Map of Irregular Varieties