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

Anca M. Mustaţǎ; Andrei Mustaţǎ

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 6, page 1739-1794
- ISSN: 1435-9855

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topMustaţǎ, Anca M., and Mustaţǎ, Andrei. "The structure of a local embedding and Chern classes of weighted blow-ups." Journal of the European Mathematical Society 014.6 (2012): 1739-1794. <http://eudml.org/doc/277759>.

@article{Mustaţǎ2012,

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 $X^\{\prime \}$, 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 $X^\{\prime \}$ allows the construction of a universally closed push-forward, and thus a comparison between the Chow groups of $X^\{\prime \}$ 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 $X^\{\prime \}$ 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.},

author = {Mustaţǎ, Anca M., Mustaţǎ, Andrei},

journal = {Journal of the European Mathematical Society},

keywords = {Deligne-Mumford stack; local embedding; etale lift; Chern classes; weighted blow-ups; moduli space of stable maps; Deligne-Mumford stack; local embedding; etale lift; Chern classes; weighted blow-ups; moduli space of stable maps},

language = {eng},

number = {6},

pages = {1739-1794},

publisher = {European Mathematical Society Publishing House},

title = {The structure of a local embedding and Chern classes of weighted blow-ups},

url = {http://eudml.org/doc/277759},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Mustaţǎ, Anca M.

AU - Mustaţǎ, Andrei

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

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 6

SP - 1739

EP - 1794

AB - 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 $X^{\prime }$, 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 $X^{\prime }$ allows the construction of a universally closed push-forward, and thus a comparison between the Chow groups of $X^{\prime }$ 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 $X^{\prime }$ 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.

LA - eng

KW - Deligne-Mumford stack; local embedding; etale lift; Chern classes; weighted blow-ups; moduli space of stable maps; Deligne-Mumford stack; local embedding; etale lift; Chern classes; weighted blow-ups; moduli space of stable maps

UR - http://eudml.org/doc/277759

ER -

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