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arXiv · 1211.0203

Remarks about bubbles

Michael McQuillan·Gianluca Pacienza
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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.

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Michael McQuillan, Gianluca Pacienza. 2012-11-01. Remarks about bubbles. https://arxiv.org/abs/1211.0203

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