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Bulletin of the American Mathematical Society

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Group actions, divisors, and plane curves


Authors: Araceli Bonifant and John Milnor
Journal: Bull. Amer. Math. Soc. 57 (2020), 171-267
MSC (2010): Primary 14L30, 14H50, 57R18, 14H10; Secondary 08A35, 14P25
DOI: https://doi.org/10.1090/bull/1681
Published electronically: February 7, 2020
MathSciNet review: 4076022
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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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Additional Information

Araceli Bonifant
Affiliation: Mathematics Department, University of Rhode Island
Address at time of publication: Institute for Mathematical Sciences, Stony Brook University
Email: bonifant@uri.edu

John Milnor
Affiliation: Institute for Mathematical Sciences, Stony Brook University
Email: jack@math.stonybrook.edu

DOI: https://doi.org/10.1090/bull/1681
Keywords: Moduli space of curves, smooth complex curves, effective $1$-cycles, stabilizers of curves, algebraic set, group actions, proper action, improper action, weakly proper action, orbifolds, weak orbifolds, rational homology manifold, tree-of-spheres, W-curves, moduli space of divisors, Deligne-Mumford compactification
Received by editor(s): March 11, 2019
Published electronically: February 7, 2020
Additional Notes: The first author wants to thank the Institute for Mathematical Sciences at Stony Brook University, where she spent her sabbatical year, for its support to this project
Article copyright: © Copyright 2020 American Mathematical Society