Monomial embeddings of the Klein curve

Abstract

The Klein curve is defined by the smooth plane model X 3 Y+ Y 3 Z+ Z 3 X=0. We give all embeddings in higher dimension with a linear action of the automorphism group. The curve has 24 flexpoints, i.e. points where the tangent intersects with multiplicity three. For even characteristic, the embeddings yield interesting configurations of the flexpoints and good linear codes.