2024/05/23 by Songbo Ling, Xin Lü, Ling, Songbo +1
Engineering · Materials Science · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Textile materials and evaluations
paper · pdf · doi:10.48550/arxiv.2405.14659
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a minimal irregular surface of general type, whose Albanese map induces a fibration f: S → C of genus g.We prove a linear upper bound on the genus g if KS2≤ 4χ(OS). Examples are constructed showing that the above linear upper bound is sharp. We also give a characterization of the Albanese fibrations reaching the above upper bound when χ(OS)≥ 5.On the other hand, we will construct a sequence of surfaces Sn of general type with KSn2/χ(OSn)>4 and with an Albanese fibration fn, such that the genus gn of a general fiber of fn increases quadratically with χ(OSn),and that KSn2/χ(OSn) can be arbitrarily close to 4.