A transversality theorem for some classical varieties (Q392221)

Let \(X\) be a homogeneous variety with an algebraic group \(G\) acting on it. Let \(Y, Z\) be subvarieties of \(X\) such that \(Z\) is smooth and \(Y\) is log canonical (resp. log terminal).NEWLINENEWLINEIt is proved that there is a non-empty open set \(U\subset G\) such that \(Y^g \times_X Z\) is log canonical (resp. log terminal) for all \(g\in U\). Here \(Y^g\) is the transition of \(Y\) by \(g\).NEWLINENEWLINEA criterion for a normal variety to be log terminal is given. Let \(f: Y\to X\) be a small resolution of a normal variety of \(X\) such that \(Y\) is smooth and \(-K_Y\) is relatively net. Then \(X\) is log terminal.