← Theoretical / proof-based

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In this program

Affine and projective varieties
Regular maps and rational maps
Birational equivalence
Dimension and tangent spaces
Smoothness
Bezout's theorem
Intersection multiplicity (introduction)
Blow-ups and resolution of singularities (overview)

Varieties and morphisms

Affine and projective varieties

Algebraic geometry · Theoretical / proof-based

Topic

Affine and projective varieties; Nullstellensatz

Practice by unit: Varieties and morphisms

Graduate Algebraic Geometry — scope drawn from open algebraic geometry notes and typical US graduate algebraic geometry syllabi.

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