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Does anyone know whether the theory of coherent systems on $K3$ surfaces has been studied and, if yes, can you give me a reference? In particular, is there an analogue of Gieseker stability and of Mumford stability for coherent systems on a $K3$? If yes, are there results concerning the smoothness and the dimension of the corresponding moduli spaces?

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Giulia will answer your question on Facebook :) –  diverietti Oct 12 '12 at 13:52

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