Lecture 10: Smooth varieties

We covered chapter 10 of Gathmann's notes.

• The tangent cone C₀X.
• The tangent space T₀X using linear forms and it's intrinsic definition as the Zariski tangent space (m/m²)^v.
• Smooth points (=regular=non-singular).
• The Jacobi conditions for smoothness.
• The implicit function theorem.

Suggested exercises: All