Group Actions, Divisors, and Plane Curves

Abstract

After a general discussion of group actions, orbifolds, and "weak orbifolds" this note will provide elementary introductions to two basic moduli spaces over the real or complex numbers: First the moduli space of effective divisors with finite stabilizer on the projective space ${\mathbb{P}}^1$ modulo the group ${\mathrm{PGL}}_2$ of projective transformations of ${\mathbb{P}}^1$; and then the moduli space of effective 1-cycles with finite stabilizer on ${\mathbb{P}}^2$ modulo the group ${\mathrm{PGL}}_3$ of projective transformations of ${\mathbb{P}}^2$.

94 pages, 30 figures