Abstract

Let $X$ be a complex projective algebraic variety with Gorenstein quotient singularities and $\mathcal {X}$ a smooth Deligne-Mumford stack having $X$ as its coarse moduli space. We show that the CSM class $c^{SM}(X)$ coincides with the pushforward to $X$ of the total Chern class $c(T_{I \mathcal{X}})$ of the inertia stack $I \mathcal {X}$. We also show that the stringy Chern class $c_{str}(X)$ of $X$, whenever it is defined, coincides with the pushforward to $X$ of the total Chern class $c(T_{II \mathcal{X}})$ of the double inertia stack $II \mathcal {X}$. Some consequences concerning stringy/orbifold Hodge numbers are deduced.

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