Moduli space of smooth n-marked genus-zero curves

Presentations

 * A smooth n-marked genus-zero curve is abstractly isomorphic to P1, with n distinct points p1,...,pn marked. If n≥3, there is a unique Mobius transformation that sends p1 to 0, p2 to 1, and p3 to \infty. Thus any smooth n-marked genus-zero curve has a canonical representative of this form; the data of the remaining marked points is parametrized by the open subset of ( C \ {0,1} )n-3 where all diagonals are removed. Thus M0n is isomorphic to ( C \ {0,1} )n-3.
 * Alternatively, PGL(2) acts freely on (P1)n \ {diagonals}, and M0n is isomorphic to the quotient.

Special cases

 * M00
 * M01
 * M02
 * M03
 * M04
 * M05
 * M06

Generalizations

 * Moduli spaces of genus-zero curves