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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Group actions, divisors, and plane curves
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by Araceli Bonifant and John Milnor HTML | PDF
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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Additional Information
  • Araceli Bonifant
  • Affiliation: Mathematics Department, University of Rhode Island
  • Address at time of publication: Institute for Mathematical Sciences, Stony Brook University
  • MR Author ID: 600241
  • Email: bonifant@uri.edu
  • John Milnor
  • Affiliation: Institute for Mathematical Sciences, Stony Brook University
  • MR Author ID: 125060
  • Email: jack@math.stonybrook.edu
  • 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
  • © Copyright 2020 American Mathematical Society
  • 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
  • MathSciNet review: 4076022