Abstract
If X is Frobenius split, then so is its normalization and we explore conditions which imply the converse. To do this, we recall that given an O X -linear map ϕ : F ⁎ O X → O X , it always extends to a map ϕ ¯ on the normalization of X. In this paper, we study when the surjectivity of ϕ ¯ implies the surjectivity of ϕ. While this doesnʼt occur generally, we show it always happens if certain tameness conditions are satisfied for the normalization map. Our result has geometric consequences including a connection between F-pure singularities and semi-log canonical singularities, and a more familiar version of the ( F-)inversion of adjunction formula.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
