Mathematical Research Letters

Volume 24 (2017)

Number 3

Finite generation of the $\log$ canonical ring for $3$-folds in char $p$

Pages: 933 – 946



Joe Waldron (DPMMS, University of Cambridge, United Kingdom)


We prove that the $\log$ canonical ring of a projective klt pair of dimension $3$ with $\mathbb{Q}$-boundary over an algebraically closed field of characteristic $p \gt 5$ is finitely generated. In the process we prove $\log$ abundance for such pairs in the case $\kappa = 2$.

Received 9 June 2015

Accepted 28 March 2016

Published 1 September 2017