A compactification of the moduli space of self-maps of \mathbbCP¹ using stable maps

2016/04/29 by Schmitt, Johannes
#14D23 #14L30 #37F10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.08917

Abstract

We present a new compactification M(d,n) of the moduli space of self-maps of \mathbbCP¹ of degree d with n markings. It is constructed via GIT from the stable maps moduli space ar M_0,n(\mathbbCP¹ × \mathbbCP¹, (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) \dashrightarrow M(d^m,n) and we give a geometric way to extend this rational map to parts of the boundary of M(d,n).

Related

• Alternate compactifications of the moduli space of genus one maps
• Compactifying the space of stable maps
• The Geometry of Stable Quotients in Genus One
• Moduli space of stable maps to projective space via GIT
• Complete moduli for fibered surfaces