families of K3 surfaces parameterized by Hermitian half spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540038
• 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, 総合研究部, 准教授 (20362056)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: テータ関数 / クンマー曲面 / モジュラー多様体 / ワイル群

Outline of Final Research Achievements

We gave explicit equations of smooth Jacobian Kummer surfaces of degree 8 in the five dimensional projective space by theta functions. As byproducts, we wrote down Rosenhain's 80 hyperpanes and 32 lines on these Kummer surfaces explicitly. Moreover we studied the fibration of Kummer surfaces over the Satake compactification of the Siegel modular 3-fold of level (2,4). The total space is a smooth projective 5-fold which is regarded as a higher-dimensional analogue of Shioda's elliptic modular surfaces.
We also studied a modular 4-fold that are realized as a W(E6)-invariant hypersurface in the five dimensional projective space.

Free Research Field

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