摘要：Fano manifolds are (complex) projective manifolds whose canonical class is anti-ample. It is now well-known that every Fano manifold is simply connected. In birational geometry, the notion of Fano manifolds is generalized to that of Fano log pairs, which allows singularities coming up naturally in the minimal model program. Correspondingly, the simple-connectedness of Fano pairs with log canonical singularities were proven by work of several authors.
In this talk, I will report on a further generalization in this direction, saying that any union of slc strata of a Fano log pair with semi-log-canonical singularities is simply connected. In particular, Fano log pairs with semi-log canonical singularities are simply connected. This is joint work with Osamu Fujino.