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I am learning stability conditions for derived categories of coherent sheaves, following Bridgeland, and coming from a vector bundles background. $\mu$-stability for vector bundles has a clear GIT origin (see Giesecker or the book of Mukai on invariants), hence I wonder if one could see the spaces of staibility conditions defined by Bridgeland as some sort of variation of GIT. Is it possible to draw such a connection?

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    $\begingroup$ I'm not an expert, so I won't attempt to give a full answer, but for instance you can see the paper homepages.math.uic.edu/~coskun/hilbbridge-1.pdf for an example in which the two are closely linked. $\endgroup$
    – user5117
    Aug 24, 2012 at 19:24

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