Remarks about bubbles
Algebraic Geometry
2012-11-02 v1 Complex Variables
Abstract
We make some remarks about bubbling on, not necessarily proper, champs de Deligne-Mumford, i.e. compactification of the space of mappings from a given (wholly scheme like) curve, so, in particular, on quasi-projective projective varieties. Under hypothesis on both the interior and the boundary such as Remark \ref{rmk:interior} below, this implies an optimal logarithmic variant of Mori's Bend-and-Break. The main technical remark is \ref{thm:logMM}, while our final remark, the cone theorem, \ref{rmk:cone}, is a variant.
Cite
@article{arxiv.1211.0203,
title = {Remarks about bubbles},
author = {Michael McQuillan and Gianluca Pacienza},
journal= {arXiv preprint arXiv:1211.0203},
year = {2012}
}
Comments
13 pages, 3 figures