On an efficient induction step with \(\text{Nklt}(X,D)\) - notes to Todorov (Q1940481)

In the paper under review, the author improves the results of \textit{G. Todorov} [Ann. Inst. Fourier 57, No. 4, 1315--1330 (2007; Zbl 1122.14031)] and \textit{L. Di Biagio} [Math. Proc. Camb. Philos. Soc. 152, No. 1, 9--34 (2012; Zbl 1232.14024)] by showing that if \(X\) is a smooth complex projective variety of general type and dimension \(3\) (resp. \(4\)) then \(|3K_X|\) (resp. \(|73K_X|\)) defines a birational map if \({\text{vol}}(K_X)>12^3\) (resp. \({\text{vol}}(K_X)>12^5\)).