M/E23

For a (not necessarily convex) polygon with n vertices in the projective plane we consider the intersection points of the lines containing the edges, which are not the vertices. If no three of these lines have a common point, then there is a unique curve of degree n-3 going through these residual points, called the adjoint curve. If the polygon is real and convex, then the adjoint curve is a hyperbolic curve. For a given hyperbolic cubic we give a method constructing all associated hexagons. Furthermore we characterize when this construction gives convex hexagons. If time permits we present how we use intersection theory to prove that a very general quartic is adjoint to exactly 864 heptagons.

M. Sc. Jannik Wesner

TU Dortmund