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Dubrovin conjecture says, roughly speaking, that the quantum cohomology of a variety $X$ is semisimple if and only if it is a good Fano [good means that there exits a full exceptional collection in the bounded derived category of coherent sheaves of $X$] If we consider not a variety but an orbifold $Y$ and orbifold quantum cohomology, Does there exist any criteria in order to determine whether the orbifold quantum cohomology of $Y$ is semisimple?

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I don't understand how to build mirror pairs well enough to answer the question, but undoubtedly a closely related question is what does the mirror of your orbifold look like? –  Daniel Pomerleano Nov 17 '10 at 20:15

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