- Local properties of algebraic varieties
- Power series expansions
- Properties of nonsingular points
- Birational maps
- Normal varieties and normalization
- Differential forms
Students should achieve mastery of the topics listed in the minimal learning outcomes section of the Math 562 Wiki page. This means they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor.