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The structure of a local embedding and Chern classes of weighted blow-ups

Anca M. Mustaţǎ; Andrei Mustaţǎ — 2012

Journal of the European Mathematical Society

For a proper local embedding between two Deligne-Mumford stacks $Y$ and $X$ , we find, under certain mild conditions, a new (possibly non-separated) Deligne-Mumford stack $X^{'}$ , with an etale, surjective and universally closed map to the target $X$ , and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to $Y$ . Moreover, a natural set of weights on the substacks of $X^{'}$ allows the construction of a universally closed...

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