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arXiv 0709.0034math.AG
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Deligne-Mumford栈的Chern类及其粗模空间

Chern classes of Deligne-Mumford stacks and their coarse moduli spaces

Hsian-Hua Tseng

备注：
v1:Preliminary version, comments are very welcome! v2: Revised and slightly expanded version
发表信息：
American Journal of Mathematics 133 (2011), no. 1, 29--38
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摘要：

设$X$是具有Gorenstein商奇点的复射影代数簇，$\X$是以$X$为粗模空间的光滑Deligne-Mumford栈.我们表明，CSM类$c^{SM}(X)$与推进到$X$的总陈类$c(T_{I\X})$的惯性堆栈$I\X$。我们还证明了$X$的弦陈类$c_{str}(X)$，无论何时定义，都与双惯性栈$II\X$的总陈类$c(T_{II\X})$向$X$的推进一致。一些后果有关stringy/orbifold霍奇数推导。

英文摘要：

Let $X$ be a complex projective algebraic variety with Gorenstein quotient singularities and $\X$ 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 $c(T_{I\X})$ of the inertia stack $I\X$. We also show that the stringy Chern class $c_{str}(X)$ of $X$, whenever is defined, coincides with the pushforward to $X$ of the total Chern class $c(T_{II\X})$ of the double inertia stack $II\X$. Some consequences concerning stringy/orbifold Hodge numbers are deduced.

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