Resolution-independence conjecture for string-theoretic Hodge numbers

Let $X$ be a variety with mild Gorenstein singularities, and let $\widehat X_1$ and $\widehat X_2$ be smooth crepant resolutions of $X$, when such resolutions exist. Resolution-independence conjecture for string-theoretic Hodge numbers. The Hodge numbers of smooth crepant resolutions do not depend on the choice of such a resolution. The conjecture is motivated by the consistency of the physical definition of orbifold Hodge numbers and is verified in the toric case in the source. Existence of crepant resolutions is not guaranteed, particularly in dimension at least four.