Abstract
Let (S,H) be a generalized Fermat pair of the type (k,n). If F⊂S is the set of fixed points of the non-trivial elements of the group H, then F is exactly the set of hyperosculating points of the standard embedding S↪Pn. We provide an optimal lower bound (this being sharp in a dense open set of the moduli space of the generalized Fermat curves) for the Weierstrass weight of these points.
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