Embedding Suzuki curves in $P^4$

Abstract

In this paper, we study the projective geometry of smooth models in $\Pro^4$ of Suzuki curves, employing the Weierstrass semigroup at the only singular point of the curves. In particular, we explicitly count the hypersurfaces of $\Pro^4$ containing the smooth projective model and provide a geometric characterization of those of small degree. We also prove that the characterization cannot be extended to higher-degree hypersurfaces of $\Pro^4$.