Canonical and log canonical singularities
In this chapter we introduce the singularities – terminal, canonical, log terminal and log canonical – that appeared in connection with the minimal model program.
Section 2.1 contains the basic definitions and their fundamental properties. Whenever possible, we work with schemes, rather than just varieties over a field of characteristic 0.
Section 2.2 starts a detailed study of log canonical surface singularities. Here we focus on their general properties; a complete classification is postponed to Section 3.3.
Ramified covers are studied in Section 2.3. This method gives a good theoretical framework to study log canonical singularities and their deformations in all dimensions, as long as the degree ...