Projective generationSyzygyWe investigate the relationship between rational plane curves and the envelopes defined by the syzygies of their parameterizations.doi:10.1016/j.jalgebra.2015.01.001Casas-AlveroDepartament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;...
except for the anticanonical embedding of, are obtained as the blow-up of the projective plane inpoints of which no three are collinear, no six lie on a conic (here). After his classification these surfaces bear his name.
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In this note we are looking after nilpotent projective curves without embedded points, which have rational normal curves of degree d as support, are defined (scheme-theoretically) by quadratic equations, have degree 2 d and have only linear syzygies. We show that, as expected, no such curve...