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

Tritangents and Their Space Sextics

Türkü Özlüm Çelik, Avinash Kulkarni, Yue Ren and Mahsa Sayyary Namin


Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve in $\mathbb{P}^3$ and that every space sextic curve has exactly 120 tritangents corresponding to its odd theta characteristics. In this paper we revisit both results from the computational perspective. Specifically, we give an algorithm to construct space sextic curves that arise from blowing up $\mathbb{P}^2$ at eight points and provide algorithms to compute the 120 tritangents and their Steiner system of any space sextic. Furthermore, we develop efficient inverses to the aforementioned methods. We present an algorithm to either reconstruct the original eight points in $\mathbb{P}^2$ from a space sextic or certify that this is not possible. Moreover, we extend a construction of Lehavi which recovers a space sextic from its tritangents and Steiner system. All algorithms in this paper have been implemented in magma.

MSC Codes:
14Q05, 14H50
algebraic curves, del Pezzo surfaces, theta characteristics, space sextic, tritangents

Related publications

2019 Repository Open Access
Türkü Özlüm Celik, Avinash Kulkarni, Yue Ren and Mahsa Sayyary Namin

Tritangents and their space sextics

In: Journal of algebra, 538 (2019), pp. 290-311