Class schedule
Week 1: Hilbert basis theorem, Noether normalization, Hilbert's Nullstellensatz, affine algebraic sets, Zariski topology
Week 2: affine algebraic varieties, regular/rational functions, projective varieties, projective Nullstellensatz,
Week 3: dimension, Krull's Hauptidealsatz, Hilbert polynomial, morphism of quasi-projective algebraic varieties
Week 4: regular functions on varieties, coordinate rings, affine cones, products of varieties, Segre embedding
Week 5: separatedness, Grassmannian, finite morphisms, Zariski's main theorem
Week 6: degree of projective varieties, dimension of fibers, Chevalley's theorem, semicontinuity, complete varieties
Week 7: incidence correspondence, criterion of irreducibility, cubic surfaces
Week 8: (projective) tangent spaces/bundles, smoothness, (projective) Jacobian criterion, Bertini's theorem
Week 9: normal varieties, blow-ups, resolution of singularities, degree revisited, intersections numbers
Week 10: Bezout's theorem, Gauss maps, dual varieties, examples of curves
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Week 11: sheaves and schemes
Week 12: basic properties of morphisms, separatedness, properness
Week 13: (*Thanksgiving) sheaves of modules, (quasi) coherent sheaves
Week 14: divisors, projective morphisms
Week 15: sheaf of differentials