Open Access
July, 2014 On Jacobian Kummer surfaces
J. Math. Soc. Japan 66(3): 997-1016 (July, 2014). DOI: 10.2969/jmsj/06630997


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.


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Kenji KOIKE. "On Jacobian Kummer surfaces." J. Math. Soc. Japan 66 (3) 997 - 1016, July, 2014.


Published: July, 2014
First available in Project Euclid: 24 July 2014

zbMATH: 1318.14042
MathSciNet: MR3238326
Digital Object Identifier: 10.2969/jmsj/06630997

Primary: 14K25
Secondary: 14J28

Keywords: Kummer surfaces , Theta functions

Rights: Copyright © 2014 Mathematical Society of Japan

Vol.66 • No. 3 • July, 2014
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