Algebraic Geometry

Prof. Barbara Fantechi

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