Journal of the Mathematical Society of Japan

On Jacobian Kummer surfaces

Kenji KOIKE

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 24 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1406206981

Digital Object Identifier
doi:10.2969/jmsj/06630997

Mathematical Reviews number (MathSciNet)
MR3238326

Zentralblatt MATH identifier
1318.14042

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

Keywords
theta functions Kummer surfaces

Citation

KOIKE, Kenji. On Jacobian Kummer surfaces. J. Math. Soc. Japan 66 (2014), no. 3, 997--1016. doi:10.2969/jmsj/06630997. https://projecteuclid.org/euclid.jmsj/1406206981


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