LGRT 1681
An elliptic pair (X,C) is a projective rational surface X with log terminal singularities, and an irreducible curve C contained in the smooth locus of X, with arithmetic genus 1 and self-intersection 0. Certain “good” polygons give rise to elliptic pairs (X,C) after a blowup. Adding another condition on the group structure of Pic^0(C) gives something called a “Lang-Trotter polygon”, in which it has been shown that Eff(X) is non-polyhedral. It has been shown that there are no Lang-Trotter triangles. Furthermore, it's known that infinite families of Lang-Trotter pentagons and heptagons exist, for instance. But what about quadrilaterals? This will be the topic of my study.