Stable logarithmic maps to Deligne-Faltings pairs I

By Qile Chen. 2010

179 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06406119da68af8a477f8beaa47da41f70a54b0f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Orbifold techniques in degeneration formulas (2011, methodology): “e induced by the natural log structures, with a degeneration formula worked out by Q. Chen in [Chen1] and virtual localization worked out by Molcho and Routis [MR]. M. Gross and B. Siebert [GS], Chen [Chen] and Abramovich and Chen [AC] have developed a logarithmic theory without expansions. These ap”
Brill-Noether theory for curves of a fixed gonality (2017, methodology): “The proof of the main lifting theorems, as well as the analysis of generic chains of cycles in the following section, will use the geometry of logarithmic prestable maps to toric varieties [2, 17, 30] and their relationship to Berkovich geometry [49, 48, 54].”
Stable logarithmic maps to Deligne-Faltings pairs II (2014, methodology): “This point of view will be a useful tool in [AC11], where we reduce the case with generalized DF-log structure on the target to the case of this paper.”