A compactification of the moduli space of self-maps of CP¹ using stable maps

Original · EN

We present a new compactification M(d,n) of the moduli space of self-maps of CP¹ of degree d with n markings. It is constructed via GIT from the stable maps moduli space ar M₀,ₙ(CP¹ × CP¹, (1,d)). We show that it is the coarse moduli space of a smooth Deligne-Mumford stack and we compute its rational Picard group. Using the recursive boundary structure inherited from the stable maps space, we give an explicit algorithm for computing top-intersection numbers of divisors on M(d,n). We also study the m-fold iteration map M(d,n) M(dᵐ,n) and we give a geometric way to extend this rational map to parts of the boundary of M(d,n).