A general elephant is a general member S in the linear system |-K_X|. It is expected that S, if exists, has good singularities whenever so does X. This problem is related to classification of Fano varieties as well as extremal neighborhoods in the local case.A classic theorem of M. Reid asserts that S is a K3 with at most  Du Val singularities if X is a Gorenstein canonical threefold with nef and big anticanonical divisor. In this talk, we will discuss the  proof of this theorem.

Reference

M. Reid, ”Projective morphisms according to Kawamata”, Warwick preprint, 1983(unpublished) www.maths.warwick.ac.uk/ miles/3folds/Ka.pdf