\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR } % \MRhref is called by the amsart/book/proc definition of \MR. \providecommand{\MRhref}[2]{% \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2} } \providecommand{\href}[2]{#2} \begin{thebibliography}{Ogu01} \bibitem[GD64]{EGA_IV} Alexander Grothendieck and Jean Dieudonn\'e, \emph{\'el\'ements de g\'eom\'etrie alg\'ebrique iv}, Inst. Hautes \'Etudes Sci. Publ. Math., 1964. \bibitem[Kat89]{KKato} Kazuya Kato, \emph{Logarithmic structures of fontaine-illusie, in:algebraic analysis, geometry, and number theory\textit{(Baltimore,MD,1988)}}, Johns Hopkins Univ.Press, Baltimore, MD (1989), 191--224. \bibitem[Kat94]{ToricSing} \bysame, \emph{Toric singularities}, American Journal of Mathematics \textbf{116} (1994), no.~5, 1073--1099. \bibitem[Ogu01]{Ogus} Arthur Ogus, \emph{Lectures on logarithmic algebraic geometry}, TeXed notes, 2001. \bibitem[Ols05]{LogCot} Martin~C. Olsson, \emph{The logarithmic cotangent complex}, Math. Ann. \textbf{333} (2005), 859--931. \end{thebibliography}