TL;DR
This paper provides explicit equations for smooth Jacobian Kummer surfaces using theta functions, enabling detailed descriptions of their geometric features such as hyperplanes and lines.
Contribution
It offers the first explicit theta function-based equations for Jacobian Kummer surfaces, including descriptions of hyperplanes and lines.
Findings
Explicit equations for Jacobian Kummer surfaces
Descriptions of Rosenhain's hyperplanes and lines
Enhanced understanding of surface geometry
Abstract
We give explicit equations of smooth Jacobian Kummer surfaces of degree 8 by theta functions. As byproducts, we can write down Rosenhain's 80 hyperpanes and 32 lines on these Kummer surfaces explicitly.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons