Consider a fixed smooth algebraic curve $C$ over $\mathbb C$. It is well-known that $\mathbb CP^3$ contains curves that are abstractly isomorphic to $C$. What is the minimal degree of a curve in $\mathbb CP^3$, abstractly isomorphic to $C$, which is not on any cubic surface?
What is the minimal degree of a smooth curves which is not on a cubic surface in $P^3$?
Nikita Kalinin
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