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A motivic change of variables formula for Artin stacks
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abstract
Let $\mathcal{X} \to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\mathcal{X}$. With a view toward the study of stringy Hodge numbers, this change of variables formula leads to a new notion of crepantness for the map $\mathcal{X} \to Y$ that coincides with the usual notion in the special case that $\mathcal{X}$ is a scheme.
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Cited by 1 Pith paper
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The dimension threshold for Batyrev's non-negativity conjecture on stringy Hodge numbers
Batyrev's non-negativity conjecture on stringy Hodge numbers is true for Gorenstein canonical projective varieties in dimension at most 4 and false in all dimensions 5 and higher.
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