Stable logarithmic maps to Deligne-Faltings pairs I

Qile Chen

Stable logarithmic maps to Deligne-Faltings pairs I

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arxiv 1008.3090 v4 pith:KUHU5JOR submitted 2010-08-18 math.AG

Stable logarithmic maps to Deligne-Faltings pairs I

Qile Chen This is my paper

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keywords stablemapslogarithmicsensecompactificationdegenerationdeligne-faltingsexpanded

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We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps is stable in the usual sense.

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Cut and paste invariants of moduli spaces of stable maps to toric surfaces
math.AG 2026-04 unverdicted novelty 6.0

A chamber decomposition of tangency conditions for log stable maps to toric surfaces makes the Grothendieck class of the moduli space constant within chambers defined by fixed cyclic orderings.