Studies of the geography of fibrations of algebraic curves from the theory of higher degree coverings and muduli spaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04833
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Ube National College of Technology
• Principal Investigator: Ishida Hirotaka 宇部工業高等専門学校, 一般科, 教授 (30435458)
• Co-Investigator(Renkei-kenkyūsha): ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203) ; SHIRANE Taketo 宇部工業高等専門学校, 一般科, 准教授 (70615161)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 代数曲面 / 代数曲線束 / 高次被覆 / 曲面特異点 / モジュライ空間

Outline of Final Research Achievements

We study the problem of the geography of fibrations of algebraic curves which is the question of which triplets of the relative Euler-Poincare characteristic, the self-intersection number of the relative canonical divisor and the genus of a fiber can occur for surfaces of general type with a fibration over smooth projective algebraic curve. By using the theory of triple coverings and Galois quadruple coverings, we give inequalities among these invariants for fibrations of Clifford index 1 and 2. Also we prove the existence of many fibrations of algebraic curves by newly developed methods for constructing the coverings of the projective line bundles.

Free Research Field

代数幾何学