Peer-Reviewed Journal Details
Mandatory Fields
Mustata, AM;Mustata, A
2012
January
Journal of the European Mathematical Society
The structure of a local embedding and Chern classes of weighted blow-ups
Validated
WOS: 3 ()
Optional Fields
MODULI SPACES STACKS
14
1739
1794
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 Chem 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 Chem classes of the stable map spaces.
ZURICH
1435-9855
10.4171/JEMS/346
Grant Details