Finite equivalence relations
In this chapter we study general questions about geometric quotients by the finite set theoretic equivalence relations that were used in Chapter 5. These results are somewhat technical and probably the best introduction is to study the examples (9.7) and (9.61). While they do not help with the proofs, they show that the questions are quite subtle and that the theorems are likely to be optimal.
Section 9.1 studies the existence question for geometric quotients. Usually they do not exist, but we identify some normality and seminormality properties of stratified spaces that ensure the existence of quotients (9.21).
The finiteness of equivalence relations is studied in Section 9.4.
The seminormality of subvarieties ...