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

• Autores: Anca M. Mustata, Andrei Mustata
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 14, Nº 6, 2012, págs. 1739-1794
• Idioma: inglés
• DOI: 10.4171/jems/346
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• Resumen

  • 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.