Real Space Sextics and their Tritangents

Kulkarni, Avinash; Ren, Yue; Sayyary Namin, Mahsa; Sturmfels, Bernd

Abstract

The intersection of a quadric and a cubic surface in 3-space is a canonical curve of genus 4. It has 120 complex tritangent planes. We present algorithms for computing real tritangents, and we study the associated discriminants. We focus on space sextics that arise from del Pezzo surfaces of degree one. Their numbers of planes that are tangent at three real points vary widely; both 0 and 120 are attained. This solves a problem suggested by Arnold Emch in 1928.

Citation

Kulkarni, A., Ren, Y., Sayyary Namin, M., & Sturmfels, B. (2018). Real Space Sextics and their Tritangents. . https://doi.org/10.1145/3208976.3208977

• Conference Name: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation
• Acceptance Date: Jun 11, 2018
• Online Publication Date: Jul 11, 2018
• Publication Date: Jul 11, 2018
• Deposit Date: May 16, 2023
• Volume: 18
• Pages: 247–254
• ISBN: 9781450355506
• DOI: https://doi.org/10.1145/3208976.3208977
• Public URL: https://durham-repository.worktribe.com/output/1133861