English

Stable logarithmic maps to Deligne-Faltings pairs I

Algebraic Geometry 2011-02-24 v4

Abstract

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.

Keywords

Cite

@article{arxiv.1008.3090,
  title  = {Stable logarithmic maps to Deligne-Faltings pairs I},
  author = {Qile Chen},
  journal= {arXiv preprint arXiv:1008.3090},
  year   = {2011}
}

Comments

We changed the terminology "log stable maps" to "stable log maps". A gap in the proof of compatibility with formal completions pointed out by Professor Bernd Siebert has been fixed, see Section 2.7. Few minor changes in Lemma 3.3.8 and the proof of Lemma 6.5.1 are made