English

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.

Keywords

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

R2 v1 2026-06-21T22:31:38.530Z