In this article we prove that the Kawamata-Viehweg vanishing theorem holds for regular del Pezzo surfaces over imperfect ground fields of characteristic $p>3$.
The author was partially supported by the AMS-Simons Travel Grant Award.
I learned about this problem in a conversation with Professor Paolo Cascini at the `Conference in Birational Geometry' at the Simons Foundation in New York (August 21-25, 2017). I am grateful to Professor Cascini for our discussion. I would also like to thank the organizers of the conference and Simons Foundation for their hospitality during the conference. My special thanks go to Professor Burt Totaro, Joe Waldron and Fabio Bernasconi for carefully reading an early draft and pointing out some mistakes.
"Kawamata-Viehweg Vanishing Theorem for del Pezzo Surfaces over imperfect fields of characteristic $p>3$." Osaka J. Math. 58 (2) 477 - 486, April 2021.