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We prove that the zero-fiber of the moment map of a totally negative quiverhas rational singularities. Our proof consists in generalizing dimension boundson jet spaces of this fiber, which were introduced by Budur. We also transferthe rational singularities property to other moduli spaces of objects in2-Calabi-Yau categories, based on recent work of Davison. This has interestingarithmetic applications on quiver moment maps and moduli spaces of objects in2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptoticbehaviour of countings of jets of quiver moment maps over finite fields.Moreover, we interpret the limit of countings of jets on a given moduli spaceas its p-adic volume under a canonical measure analogous to the measure builtby Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves.

Rational singularities for moment maps of totally negative quivers