TITLE: Singularities of pairs
QUESTION [12 upvotes]: In the next days I have to give a talk in which I need to explain some of the usual singularities of pairs that one meets when dealing with the minimal model program: KLT, DLT and LC pairs.
In particular I would like to give an intuition (also to non specialists) of the reason why an LC pair is much more difficult to treat than a DLT pair, for example.
In the same context I would also like to give an intuition of what the LC centers of a pair are and why they are "special" subvarieties for a pair.
Note that I'm always considering normal (possibly non-smooth) projective varieties. 
Do you have any ideas?

REPLY [3 votes]: I know very little of this subject, but I can attest to the value of it, since many of us studied the singularities of theta divisors for years without noticing or even conjecturing some basic results that followed from Kolla'r's observation that (A,D) is a log canonical pair if D is a theta divisor on a principally polarized abelian variety A.  As Kolla'r put it with extreme simplicity and clarity: "we know a highly singular divisor moves, but a theta divisor doesn't move, so it should not be very singular."  He deduced that the points of D of multiplicity ≥ k have codimension ≥ k in A.  I particular there are no points on D of multiplicity > dim(A). The generalization of this result by Ein and Lazarsfeld that the extreme case occurs only for a product p.p.a.v., established the normality of an irreducible theta divisor.  To me, this is a beautiful example of the concept of l.c. pairs which allowed the characterization of indecomposable p.p.a.v's in terms of the geometry of their theta divisors.  This is one of the first cases of a technique that allowed the analysis of theta divisors that could not be understood in terms of curves, e.g. as Jacobians or Pryms.