Embedding Suzuki curves in ℙ⁴

2012/12/10 by Edoardo Ballico, Ballico, Edoardo, Alberto Ravagnani +1
Mathematics · #14G17 #14H50 #14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14G17 #msc:14H50 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.1212.2091

arxiv created 2012/12/10 · arxiv updated 2012/12/11

Abstract

Here we study the projective geometry of smooth models X_n ⊆ ℙ⁴ of plane Suzuki curves S_n. The knowledge of a system of generators for the Weierstrass semigroup at the only singular point of the curve is shown to have relevant geometric consequences. In particular, here we explicitly count the hypersurfaces of ℙ⁴ containing X_n and provide a geometric characterization of those of small degree. We prove that the characterization cannot be extended to higher-degree hypersurfaces of ℙ⁴.

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