Study on K3 modular forms derived from hypergeometric systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04807
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: Shiga Hironori 千葉大学, 大学院理学研究院, 名誉教授 (90009605)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: K3 曲面 / 保型関数 / 超幾何微分方程式 / 虚数乗法論

Outline of Final Research Achievements

In the 19th century, Gauss, Abel and Jacobi constructed the theory of elliptic curves and their moduli. It had a big influence in mathematics of 20th century. At present, it is developed to the higher dimensional analogues. The K3 surface is the 2-dimensional analogue of the elliptic curve.
On the other hand, Hilbert proposed his 12th problem in 1901, it was an important proposal in number theory. In 1960's, Shimura gave a big contribution for this problem. But the Hilbert 12th problem iself is still open. In our research project, we could give a visualization of Shimura's theory and constructed a series of explicit examples.

Free Research Field

数学とくに代数学