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arXiv · 1701.02353

Tritangent planes to space sextics: the algebraic and tropical stories

Corey Harris·Yoav Len
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Abstract

We discuss the classical problem of counting planes tangent to general canonical sextic curves at three points. We determine the number of real tritangents when such a curve is real. We then revisit a curve constructed by Emch with the greatest known number of real tritangents, and conversely construct a curve with very few real tritangents. Using recent results on the relation between algebraic and tropical theta characteristics, we show that the tropicalization of a canonical sextic curve has 15 tritangent planes.

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Corey Harris, Yoav Len. 2017-01-09. Tritangent planes to space sextics: the algebraic and tropical stories. https://doi.org/10.1007/978-1-4939-7486-3_3

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