Plane curves whose tangent lines at collinear points are concurrent

Abstract

Abstract.We are interested in a particular geometry of plane curves in characteristic p > 0, which was inspired by Thas's article [13]. We will prove that any plane curve of degree > 2 whose tangent lines at collinear points are concurrent is either a strange curve or projectively equivalent to the Fermat curve of degree q + 1, where q is a power ofp.Mathematics Subject Classifications (1991): Primary 14N05; secondary 51N05, 14H99.

Algebraic webs invariant under endomorphisms

“…where χ(A) is the topological Euler characteristic of A. This is proved using the Riemann-Hurwitz formula as in [GH,; see also [Ho,p. 289].…”