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Remarks about bubbles

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arxiv 1211.0203 v1 pith:26ML4E56 submitted 2012-11-01 math.AG math.CV

Michael McQuillan , Gianluca Pacienza This is my paper · ORCID
classification math.AGmath.CV
keywords remarkconeinteriorremarksvariantbelowbend-and-breakboundary
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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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    math.AG 2019-08 accept novelty 7.0 of 10

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