Abstract:In this article, we study isomorphisms between complements of irreducible
curves in the projective plane $\mathbb{P}^2$, over an arbitrary algebraically
closed field. Of particular interest are rational unicuspidal curves. We prove
that if there exists a line that intersects a unicuspidal curve $C \subset
\mathbb{P}^2$ only in its singular point, then any other curve whose complement
is isomorphic to $\mathbb{P}^2 \setminus C$ must be projectively equivalent to
$C$. This generalizes a result of H. Yoshihara wh… Show more
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