2019/01/31 by Zhi Jiang, Jiang, Zhi
Mathematics · #14D06 #14E99 (Secondary) #14J40 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1901.11207
openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Severi type inequalities for big line bundles on irregular varieties via cohomological rank functions. We show that these Severi type inequalities on an irregular variety X are related to some natural defined birational invariants of a general fiber F of the Albanese morphism of X. As applications, we provide a new lower bound of volumes of irregular threefolds, a sharp lower bound of varieties of maximal Albanese dimension and of general type, and show that the canonical model of such a variety with the minimal volume should be a flat double covers of a principally polarized abelian variety (A, Θ) branched over D∈ |2Θ|.