Algebraic Geometry I
Algebraic varieties: definition, affine and projective varieties, examples. Products, fibered products. Separatedness and completeness. Irreducibility and dimension theory. Tangent spaces and differentials. Smoothness. Schemes: definition, affine and projective schemes, examples. Reduced schemes and varieties. Products and fibered products. Coherent, locally free, invertible sheaves. Cotangent sheaf. [Possibly] Smooth projective curves, correspondence divisors/invertible sheaves, Serre duality, Riemann-Roch, applications.
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