Log canonical models of foliated surfaces

Yen-An Chen

Log canonical models of foliated surfaces

Algebraic Geometry 2022-02-25 v2

Authors: Yen-An Chen

Abstract

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of separatedness and properness and a property related to local-closedness for the moduli functor $\mathcal{S}_P^{sm}$ which parametrizes the stable smoothable foliated surface pairs. On the way, we also show a result on the invariance of plurigenera.

Keywords

foliated surfaces log canonical models general type bounded moduli moduli functor plurigenera invariance

Cite

@article{arxiv.2103.12669,
  title  = {Log canonical models of foliated surfaces},
  author = {Yen-An Chen},
  journal= {arXiv preprint arXiv:2103.12669},
  year   = {2022}
}

Comments

46 pages and 5 figures. Title is changed in order to be more clear. Some revisions are made accordingly. Any comments are very welcomed. arXiv admin note: text overlap with arXiv:1912.02931

Log canonical models of foliated surfaces

Abstract

Keywords

Cite

Comments

Related papers