Topological Classification of Cubic Surfaces in Three-Dimensional Real Projective Space based on Julia Implementations: 5 Case Studies (German)

This article shows how Julia and computer algebra tools classify topological types of real cubic surfaces in projective space. The code extends in the webisite and was developed during an internship at the Institute of Geometry, TU Dresden (June 23 – July 4, 2025).

It includes singularity computation, smoothness checks, and counting connected components, with five examples.

Complete correctness isn’t guaranteed beyond verified linear transformations. Work was done independently using open-source software. The code supports teaching and research.

Thanks to Professor Mario Kummer for his support.

Here is the GitHub repository, which contains detailed usage instructions and the corresponding Julia code examples.

Recommended citation: Yimu Mao. (2025). ".Topologische Klassifikation kubischer Flächen im dreidimensionalen reellen projektiven Raum anhand von Julia-Implementierungen: 5 Fallbeispiele "
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