In this chapter we collect several topics for which good references are either not available or are too scattered in the literature.
In Section 10.1 we prove three well-known results on birational maps of surfaces for excellent 2-dimensional schemes.
General properties of seminormal schemes are studied in Section 10.2. Seminormality plays a key role in the study of lc centers and in many inductive methods involving lc and slc pairs.
In Section 10.3 we gather, mostly without proofs, various vanishing theorems that we use. Section 10.4 contains resolution theorems that are useful for non-normal schemes and in Section 10.5 we study the action of birational maps on differential forms. The basic theory of cubic hyperresolutions ...