Journal of the Mathematical Society of Japan

On Jacobian Kummer surfaces


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We give explicit equations of smooth Jacobian Kummer surfaces of degree 8 in $\mathbb P^5$ by theta functions. As byproducts, we can write down Rosenhain's 80 hyperplanes and 32 lines on these Kummer surfaces explicitly. Moreover we study 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.

Article information

J. Math. Soc. Japan, Volume 66, Number 3 (2014), 997-1016.

First available in Project Euclid: 24 July 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14K25: Theta functions [See also 14H42]
Secondary: 14J28: $K3$ surfaces and Enriques surfaces

theta functions Kummer surfaces


KOIKE, Kenji. On Jacobian Kummer surfaces. J. Math. Soc. Japan 66 (2014), no. 3, 997--1016. doi:10.2969/jmsj/06630997.

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