Smoothness criterion for Fano orbifolds and bases of Lagrangian fibrations

Abstract

We establish a smoothness criterion for Fano varieties with quotient singularities. As an application, we show that if $X\to B$ is a Lagrangian fibration from a compact hyper-Kähler manifold and $B$ has quotient singularities, then $B$ is a projective space.

arXiv comment13 pages, comments are very welcome!