MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Real Space Sextics and their Tritangents

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


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.

Dec 20, 2017
Jan 4, 2018

Related publications

2018 Repository Open Access
Avinash Kulkarni, Yue Ren, Mahsa Sayyary Namin and Bernd Sturmfels

Real space sextics and their tritangents

In: ISSAC '18 proceedings of the 43rd international symposium on symbolic and algebraic computation ; New York, USA, July 16-19, 2018
New York : ACM, 2018. - pp. 247-254