PUB - Publikationen an der Universität Bielefeld

This paper further studies the matroid realization space of a specific deformation of the regular n-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular surfaces $\Xi _{1}(n)$ over the modular curve $X_1(n)$ . Here, we focus on the peculiar cases when $n=7,8$ in more detail. We obtain concrete quartic surfaces in $\mathbb {P}<^>3$ equipped with a dominant rational self-map stemming from an operator on line arrangements, which yields K3 surfaces with a dynamical system that is semi-conjugated to the plane.