2013/04/22 by Xinyi Yuan, Tong Zhang, Yuan, Xinyi +1
Mathematics · #14C20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14C20
paper · pdf · doi:10.48550/arxiv.1304.6122
27 pages
arxiv created 2013/04/22 · openalex publication_date 2013/04/22 · arxiv updated 2013/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic. It can be viewed as a relative version of the classical Noether inequality for surfaces. As a consequence, we give a new proof of the slope inequality for fibered surface without using any stability method. The treatment is essentially different from these of Xiao, Cornalba--Harris and Moriwaki. We also study the geography problem of surfaces in positive characteristics and show that the Severi inequality is true for surfaces of general type in positive characteristic whose Albanese map is generically finite. Moreover, the geography of surfaces with Albanese fibrations is studied.