Die Automorphismengruppe der ebenen reellen Polynomgeometrie. (The automorphism group of the planar real polynomial geometry) (Q803935)

We have an incidence structure in which the points are ordered pairs (x,y) of elements of the reals and the blocks are sets of points satisfying polynomial equations \(y=f(x)\). Two blocks are said to be parallel if the polynomials differ by a constant. The author shows that automorphisms of this system are homomorphisms of \({\mathbb{R}}^ 2\) and preserve parallelism. The author determines the full automorphism group of this incidence system. He also looks at polynomial systems over arbitrary infinite fields.