Tropical Geometry for Sextic Curves
Published:Dec 30, 2025 15:04
•1 min read
•ArXiv
Analysis
This paper leverages tropical geometry to analyze and construct real space sextics, specifically focusing on their tritangent planes. The use of tropical methods offers a combinatorial approach to a classical problem, potentially simplifying the process of finding these planes. The paper's contribution lies in providing a method to build examples of real space sextics with a specific number of totally real tritangents (64 and 120), which is a significant result in algebraic geometry. The paper's focus on real algebraic geometry and arithmetic settings suggests a potential impact on related fields.
Key Takeaways
- •Applies tropical geometry to the problem of finding tritangent planes of space sextics.
- •Provides a method for constructing real space sextics with a specific number of totally real tritangents.
- •The method involves lifting tropical tritangents and analyzing their properties over quadratic extensions.
- •Offers insights into the arithmetic setting of the problem.
Reference
“The paper builds examples of real space sextics with 64 and 120 totally real tritangents.”