Geodesic
The structure of a local embedding and Chern classes of weighted blow-ups
Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 1739-1794.

Voir la notice de l'article provenant de la source EMS Press

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 push-forward, and thus a comparison between the Chow groups of X′ and X. We apply the construction above to the computation of the Chern classes of a weighted blow-up along a regular local embedding via deformation to a weighted normal cone and localization. We describe the stack X′ in the case when X is the moduli space of stable maps with local embeddings at the boundary. We apply the methods above to find the Chern classes of the stable map spaces.
DOI : 10.4171/jems/346
Classification : 14-XX, 00-XX
Keywords: Deligne-Mumford stack, local embedding, etale lift, Chern classes, weighted blow-ups, moduli space of stable maps 
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     title = {The structure of a local embedding and {Chern} classes of weighted blow-ups},
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Anca M. Mustaţă; Andrei Mustaţă. The structure of a local embedding and Chern classes of weighted blow-ups. Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 1739-1794. doi : 10.4171/jems/346. http://geodesic.mathdoc.fr/articles/10.4171/jems/346/

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