Holomorphic orbispheres in elliptic curve quotients and Diophantine equations (Q294141)

The authors of the paper under review calculate the quantum cohomology rings of elliptic \(P^{1}\) orbifolds by counting orbicurves. These orbifolds have elliptic curves as their manifold covers and have three singular points. They classify holomorphic orbifold curves by orbifold coverings. Then they relate coverings with lattices and use this correspondence to count curves of certain degree \(d\) as a solution of Diophantine equations involving \(d\) and the modulus of the lattice. The paper is well written and figures are used to illustrate the concepts.