Arakelov (in)equalities

2008/12/17 by Eckart Viehweg, Viehweg, Eckart
Computer Science · Mathematics · #14D05 #14D07 #14G35 (Primary) 14K10 #14J60 #32G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0812.3350

openalex publication_date 2008/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss several numerical conditions for families of projective varieties or variations of Hodge structures.

Citations

• Shimura- and Teichmueller curves
• Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

Related

• Hodge-Arakelov inequalities for family of surfaces fibered by curves
• Arakelov inequalities in higher dimensions
• Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
• Arakelov inequalities and the uniformization of certain rigid Shimura varieties
• A characterization of certain Shimura curves in the moduli stack of abelian varieties