Real Space Sextics and their Tritangents
Avinash Kulkarni, Yue Ren, Mahsa Sayyary Namin, and Bernd Sturmfels
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Submission date: 20. Dec. 2017
published 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. - P. 247 - 254
DOI number (of the published article): 10.1145/3208976.3208977
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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.