Chel’tsov, I. A.; Park, Jihun Global log-canonical thresholds and generalized Eckardt points. (English. Russian original) Zbl 1077.14016 Sb. Math. 193, No. 5, 779-789 (2002); translation from Mat. Sb. 193, No. 5, 149-160 (2002). Let \(X\) be a smooth hypersurface of degree \(n\geq 3\) in \(\mathbb P ^n\), \(Z\) be a closed subvariety of \(X\) and \((X,B)\) be a log canonical pair. For a \(\mathbb Q\)-Cartier divisor \(D\) on \(X\) the log canonical threshold of \(D\) along \(Z\) with respect to the log canonical divisor \(K_{X} + B\) is defined by \[ \text{lct}_{Z} (D;X,B)= \sup \{c:K_{X} + B + cD \text{ is log canonical along } Z\}. \] From definition it follows that \(\text{lct}_{Z} (D;X,B)\in [0,1]\). The authors prove that \(\text{lct}_{Z} (H;X,B)\) is at least \((n-1)/n\) for arbitrary hyperplane sections \(H\) on \(X\). They also show that \(\text{lct}_{Z} (H;X,B)=(n-1)/n\) if and only if \(H\) is a cone in \(\mathbb P^{(n-1)}\) over a smooth hypersurface of degree \(n\) in \(\mathbb P^{(n-2)}\). Reviewer: Georgi Hristov Georgiev (Shumen) Cited in 14 Documents MSC: 14E05 Rational and birational maps 14E30 Minimal model program (Mori theory, extremal rays) Keywords:smooth hypersurfaces; log canonical thresholds × Cite Format Result Cite Review PDF Full Text: DOI arXiv