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

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.

arXiv comment31 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