\(H^1\)-Vanishing Theorems

We describe different approaches to prove \(H^1\)-vanishing for ideal sheaves of zero-dimensional schemes. When looking for appropriate \(H^1\)-vanishing theorems for the problems discussed in Chap. 4, one has to be aware that the types of zero-dimensional schemes to be considered are quite different (cf. Sects. 2.2.1.4 and 2.3.4).