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arXiv · 0812.3101

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

Anca M. Mustata·Andrei Mustata
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Abstract

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.

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Anca M. Mustata, Andrei Mustata. 2012-04-17. The structure of a local embedding and applications to Chern classes of weighted blow-ups. https://arxiv.org/abs/0812.3101

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