Group actions, divisors, and plane curves

Bonifant, Araceli; Milnor, John

doi:10.1090/bull/1681

Group actions, divisors, and plane curves
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Bull. Amer. Math. Soc. 57 (2020), 171-267 Request permission

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 of projective transformations of $\mathbb {P}^1$; and then the moduli space of curves (or more generally effective algebraic $1$-cycles) with finite stabilizer in $\mathbb {P}^2$, modulo the group of projective transformations of $\mathbb {P}^2$. It also discusses automorphisms of curves and the topological classification of smooth real curves in $\mathbb {P}^2$.

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