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Singularities of the Minimal Model Program by Sándor Kovács, János Kollár

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2

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 ...

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