Cohomological support loci and Pluricanonical systems on irregular varieties

Zhi Jiang

Cohomological support loci and Pluricanonical systems on irregular varieties

Algebraic Geometry 2021-08-17 v1

Authors: Zhi Jiang

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 $X$ .

Keywords

irregular variety cohomological support loci pluricanonical systems albanese morphism picard variety hodge theory birationality

Cite

@article{arxiv.2108.06956,
  title  = {Cohomological support loci and Pluricanonical systems on irregular varieties},
  author = {Zhi Jiang},
  journal= {arXiv preprint arXiv:2108.06956},
  year   = {2021}
}

Related papers

View all related →