Adjunction and residues
This chapter starts the main part of the book where we aim to understand the difference between klt pairs and general lc pairs.
Once the machinery of Mori’s program was developed, it became clear that while klt pairs behave nearly as well as smooth varieties, many of the theorems and methods fail for lc pairs. Thus a separate, detailed study of lc pairs became necessary.
Furthermore, lc pairs turn out to be very useful in applications. Time and again, the solution to a question involving a smooth variety X relied on introducing an auxiliary -divisor Δ such that (X, Δ) is lc but not klt and then using the resulting exceptional ...