東京理科大学理工学部 数学科

seminar:2015:001

第01回

• 講演者 : 永野 中行 氏（早稲田大学）
• 題目 : Modular functions via $K3$ surfaces and an application in number theory
• 日時 : 平成27年5月15日（金）15:40 – 16:30

$K3$ surfaces are complex surfaces whose canonical bundles are trivial. We can regard $K3$ surfaces as 2-dimensional analogy of elliptic curves. There exist good modular functions coming from the moduli of $K3$ surfaces. Such modular functions are extensions of classical elliptic modular functions. In this talk, first, we recall basic properties of the moduli of $K3$ surfaces. Next, we will see some examples of $K3$ modular functions given by several researchers. At the last, the speaker will present a result of the Hilbert modular functions for the minimal discriminant via $K3$ surfaces. This result has applications in number theory. Namely, the period mappings of $K3$ surfaces allow us to obtain new explicit models of Shimura curves and a simple construction of class fields over quartic $CM$-fields.

seminar/2015/001.txt · 最終更新: 2017/11/16 18:27 (外部編集)