Studies of fibred complex surfaces from diversified perspectives

2016 Fiscal Year Final Research Report

• Project/Area Number: 24244002
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: Konno Kazuhiro 大阪大学, 理学研究科, 教授 (10186869)
• Co-Investigator(Kenkyū-buntansha): 大渕 朗 徳島大学, その他の研究科, 教授 (10211111) ; 徳永 浩雄 首都大学東京, 理工学研究科, 教授 (30211395) ; 小木曽 啓示 東京大学, 数理(科)学研究科(研究院), 教授 (40224133) ; 臼井 三平 大阪大学, その他部局等, 名誉教授 (90117002) ; 足利 正 東北学院大学, 工学部, 教授 (90125203)
• Project Period (FY): 2012-05-31 – 2017-03-31
• Keywords: 代数曲線束 / 堀川指数 / 自己同型 / 楕円曲面 / 対数的混合ホッジ構造 / 原始的双有理変換

Outline of Final Research Achievements

Smooth projective algebraic surfaces with a fibration over a smooth projective curve are studied through the local analytic or topological invariants such as Horikawa index and local signature. We gave an explicit formula for them for non-hyperelliptic genus 3 fibrations. Also we studied plane curve arrangements through multiple sections of relative Jacobian varieties (of small genus) and produced new examples of Zariski pairs.

Free Research Field

代数幾何学