Log-regularity of monoid algebras

Abstract

Local log-regular rings are Cohen-Macaulay local domains introduced by Kazuya Kato to expand the theory of toric varieties without a base. In this note, we show that local rings of monoid algebras over regular rings are log-regular. As a corollary, we show that monoid algebras are log-regular rings.

10 pages, added a connection between the log-regularity of non-local rings and that of log-schemes, improved Lemma 2.8, and made other minor changes