Study of algebraic curves, K3 surfaces and Abelian varieties

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04815
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Yamanashi
• Principal Investigator: KOIKE Kenji 山梨大学, 大学院総合研究部, 准教授 (20362056)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 超幾何関数 / 代数曲線 / K3曲面 / アーベル多様体

Outline of Final Research Achievements

We studied the Schwarz map with the monodromy group Δ(7,7,7), and constructed its inverse by Riemann's theta constants explicitly. To construct the Schwarz inverse, we determined the monodromy group, Riemann's period matrices and the Riemann constant with an explicit symplectic basis for associated algebraic curves. As a consequence, we gave explicit modular interpretations of the Klein quartic curve and the Fermat septic curve as modular varieties
parametrizing Abelian 6-folds with endomorphisms ZZ[z_7].

Free Research Field

代数幾何