Positivity of the CM line bundle for K-stable log Fanos

Quentin Posva

Positivity of the CM line bundle for K-stable log Fanos

Algebraic Geometry 2022-01-03 v2

Authors: Quentin Posva

Abstract

We prove the bigness of the Chow-Mumford line bundle associated to a $\mathbb{Q}$ -Gorenstein family of log Fano varieties of maximal variation with uniformly K-stable general geometric fibers. This result generalizes a recent theorem of Codogni and Patakfalvi to the logarithmic setting.

Keywords

chow-mumford line bundle log fano varieties k-stability bigness maximal variation

Cite

@article{arxiv.1910.12623,
  title  = {Positivity of the CM line bundle for K-stable log Fanos},
  author = {Quentin Posva},
  journal= {arXiv preprint arXiv:1910.12623},
  year   = {2022}
}

Comments

31 pages. Comments are welcome. v2: introduction has been rewritten to reflect recent progress in the field. Final version, to be published in Trans. of the AMS

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