I started study the moduli space theory, by Newstead's book ''Lectures on moduli problems and orbit spaces". Theorem 3.21 says that given a variety $X$ and a line bundle $L$ over $X$, then for any L-linear action of a reductive group $G$ on $X$ there exists a good quotien of semi-stable objects by the action. Later it is possible to prove that the moduli problem of classifying Giseker semistable sheaves on a projective variety admits a coarse moduli space, and the proof is made by showing that Giseker semistability is equivalent to GIT semistability. What is confusing me is the fact that I can't prove that to have a good quotient is enough to have a coarse moduli space.

Thank you in advance.


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