Elliptic fibrations on Kummer surfaces

• Project/Area Number: 20540022
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Chuo University
• Principal Investigator: KUWATA Masato Chuo University, 経済学部, 教授 (00343640)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2010: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 楕円曲面 / K3曲面 / 数論幾何学 / クンマー曲面

Research Abstract

On a K3 surface there may exist more than one elliptic fibration. In order to study detailed arithmetic properties, it is very useful to have many elliptic fibra-tions on a given K3 surface. Our objective is to classify all elliptic fibrations on a given K3 surface and describe them as explicitly as possible. We made a significant progress on this problem in the case of Kummer surfaces associated with curves of genus 2. We also ob-tained some interesting results on K3 surfaces related to modular elliptic surfaces.

Research Products

• [Presentation] Elliptic curve with isomorphic 3-torsion structure (2010)
  • Author(s): M.Kuwata
  • Organizer: Workshop on Number theory, Geometry and Physics at the crossroads, Tsuda College
  • Year and Date: 2010-08-31
• [Presentation] 3-torsion of the Jacobian of a curve of genus 2 and the Mordell-Weil lattice of a rational elliptic surface (2010)
  • Author(s): M.Kuwata
  • Organizer: Workshop on elliptic fibrations and K3 surfaces, Humboldt-Universitat zu Berlin
  • Year and Date: 2010-07-15
• [Presentation] 3-torsion of the Jacobian of a curve of genus 2 and the Mordell-Weil lattice of a rational elliptic surface (2010)
  • Author(s): 鍬田政人
  • Organizer: Workshop on elliptic fibrations and K3 surfaces
  • Place of Presentation: Humboldt-Universitat zu Berlin
  • Year and Date: 2010-07-15
• [Presentation] Elliptic curve with iso-morphic 3-torsion structure (2010)
  • Author(s): M.Kuwata
  • Organizer: Workshop on arithmetic aspects of elliptic surfaces, Hausdorff Institute, Bonn
  • Year and Date: 2010-03-12
• [Presentation] Hessian and the elliptic modular surface for level 3 (2010)
  • Author(s): 鍬田政人
  • Organizer: Workshop : Arithmetic aspects of elliptic surfaces
  • Place of Presentation: Hausdorff 研究所(ドイツ・ボン)
  • Year and Date: 2010-03-12
• [Remarks] ホームページ等
  • URL: http://c-faculty.chuo-u.ac.jp/~kuwata/
• [Remarks]
  • URL: http://c-faculty.chuo-u.ac.jp/~kuwata
• [Remarks]
  • URL: http://c-facuity.chuo-u.ac.jp/~kuwata/