Mordell-Weil lattices of elliptic K3 surfaces

• Project/Area Number: 23540028
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chuo University
• Principal Investigator: KUWATA Masato 中央大学, 経済学部, 教授 (00343640)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: K3曲面 / 楕円曲面 / 数論幾何学 / 国際研究者交流 アメリカ合衆国 / 国際研究者交流

Research Abstract

A K3 surface can have many different elliptic fibrations. Our objective is to classify all elliptic fibrations on a given K3 surface, and describe their Mordell-Weil lattices explicitly. Our principal result was the explicit description of the generators of the Mordell-Weil group of the elliptic fibration of rank 16 to 18 obtained from the Inose fibration on a Kummer surface of product type. This result was made possible through a series of discussions with Prof. Abhinav Kumar of MIT held in the U.S. and Japan during the period between 2012 and 2013.

Research Products

• [Journal Article] Vanishing and non-vanishing Dirichelet twists of L-function of elliptic curves (2012)
  • Author(s): Jack Fearnley, Hershy Kisilevsky, Masato Kuwata
  • Journal Title: Journal of London Mathematical Society Volume: 86 Pages: 539-557
• [Journal Article] Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves (2012)
  • Author(s): Jack Fearnley, Hershy Kisilevsky, Masato Kuwata
  • Journal Title: Journal of London Mathematical Society Volume: 86 Issue: 2 Pages: 539-557
  • DOI: 10.1112/jlms/jds018
  • Peer Reviewed
• [Presentation] Elliptic surface with Mordell-Weil rank 18 (2014)
  • Author(s): Masato Kuwata
  • Organizer: Intercity Number Theory Seminar in the Netherlands
  • Place of Presentation: University of Groningen
  • Year and Date: 2014-02-28
  • Invited
• [Presentation] Elliptic K3 surfaces with Mordell-Weil rank 18 (2014)
  • Author(s): Masato Kuwata
  • Organizer: Intercity Number Theory Seminar in the Netherlands
  • Place of Presentation: University of Groningen
  • Invited
• [Presentation] 3-torsion points of curves of genus 2 and rational elliptic threefolds (2012)
  • Author(s): Masato Kuwata
  • Organizer: 早稲田整数論研究集会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2012-03-21
  • Invited
• [Presentation] 3-torsion points of curves of genus 2 and rational elliptic threefolds
  • Author(s): 鍬田 政人
  • Organizer: 早稲田整数論研究集会(招待講演)
  • Place of Presentation: 早稲田大学
• [Remarks]
  • URL: http://c-faculty.chuo-u.ac.jp/~kuwata/