Globally F-regular and log Fano varieties

Citations of this article
Mendeley users who have this article in their library.


We prove that every globally F-regular variety is log Fano. In other words, if a prime characteristic variety X is globally F-regular, then it admits an effective Q{double-struck}-divisor Δ such that -KX-Δ is ample and (X,Δ) has controlled (Kawamata log terminal, in fact globally F-regular) singularities. A weak form of this result can be viewed as a prime characteristic analog of de Fernex and Hacon's new point of view on Kawamata log terminal singularities in the non-Q{double-struck}-Gorenstein case. We also prove a converse statement in characteristic zero: every log Fano variety has globally F-regular type. Our techniques apply also to F-split varieties, which we show to satisfy a " log Calabi-Yau" condition. We also prove a Kawamata-Viehweg vanishing theorem for globally F-regular pairs. © 2009 Elsevier Inc.




Schwede, K., & Smith, K. E. (2010). Globally F-regular and log Fano varieties. Advances in Mathematics, 224(3), 863–894.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free