Exercise 109.57.2 (Theorems). Precisely state a nontrivial fact discussed in the lectures related to each item.

1. on birational invariance of pluri-genera of varieties,

2. being an affine morphism is a local property,

3. the topology of a scheme theoretic fibre of a morphism, and

4. valuative criterion of properness.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).