A Transversality Theorem for some Classical Varieties

In 2009, de Fernex and Hacon proposed a generalization of the notion of the singularities to normal varieties that are not Q-Gorenstein. Based on their work, we generalize Kleiman's transversality theorem to subvarieties with log terminal or log canonical singularities. We also show that some classical varieties, such as generic determinantal varieties, W^r_d for general smooth curves, and certain Schubert varieties in G(k, n) are log terminal.