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Abstract We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces. By proving a general result on such wonderful compactifications, we conclude that this moduli space is Chow-equivalent to an explicit toric variety (whose fan can be understood as a tropical version of the moduli space), from which a computation of its Chow ring follows.
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Twistors, Hyper-Kaehler Manifolds, and Complex Moduli
A theorem of Kuranishi (Ann Math 75(2):536–577, 1962) tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli space contains a sequence of regions for which the local dimension tends to infinity. These examples naturally arise from the twistor theory of hyper-Kähler manifolds.
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- Award ID(s):
- 1510094
- PAR ID:
- 10222314
- Editor(s):
- Chiossi, Simon; Fino, Anna; Musso, Emilio; Podesta, Fabio; Vezzoni, Luigi
- Date Published:
- Journal Name:
- Springer INdAM series
- Volume:
- 23
- ISSN:
- 2281-5198
- Page Range / eLocation ID:
- 207-214
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/978-3-319-67519-0
