| 11. | The domain curve C is an element of the Deligne Mumford moduli space of curves.
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| 12. | The nerve of a category is often used to construct topological versions of moduli spaces.
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| 13. | This correction renders the moduli space nonsingular, and also leads to chiral symmetry breaking.
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| 14. | This turns \ mathcal H into a locally trivial fiber bundle over the moduli space.
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| 15. | This is notably used in the Deligne Mumford compactification of the moduli space of algebraic curves.
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| 16. | Their program is to try to construct TMF as a moduli space of supersymmetric Euclidean field theories.
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| 17. | Hyperelliptic curves also appear composing entire connected components of certain strata of the moduli space of Abelian differentials.
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| 18. | Compactification of moduli spaces generally require allowing certain degeneracies for example, allowing certain singularities or reducible varieties.
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| 19. | The Keel Mori theorem implies that an Artin stack has a coarse moduli space which is an algebraic space.
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| 20. | This gave the possibility of constructions of moduli spaces, since in general such structures depend continuously on parameters.
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