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The result is then a ''coarse moduli scheme''. Its lack of refinement is, roughly speaking, that it doesn't guarantee for families of objects what is inherent in the fine moduli scheme. As Mumford pointed out in his book ''Geometric Invariant Theory'', one might want to have the fine version, but there is a technical issue (level structure and other 'markings') that must be addressed to get a question with a chance of having such an answer.
[[Teruhisa Matsusaka]] proved a result, now known as [[Matsusaka's Big Theorem]], establishing a necessary condition on a [[moduli problem]] for the existence of a coarse moduli scheme.<ref>[https://sites.math.washington.edu/~kovacs/2013/papers/Kovacs__YPG_to_moduli.pdf S. J. Kovacs, ''Young person's guide to moduli of higher dimensional varieties'' (PDF)]
at p. 13</ref>
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