Kommutatív algebra és algebrai geometria

(Gyenge Ádám, 2026)
  1. Prime and maximal ideals, radicals, affine varieties, Hilbert's Nullstellensatz
  2. Noetherian rings, Hilbert's basis theorem, Noether-Lasker theorem, Noetherian topological spaces, irreducible components
  3. Dimension, localisation, local rings
  4. Sheaf of regular functions
  5. Ringed spaces, prevarieties, gluing, morphisms, varieties
  6. Projective varieties, homogeneous coordinates, projective Nullstellensatz,
  7. Regular functions on projective varieties, Segre and Veronese embeddings, Grassmannian, Plücker embedding
  8. Birational maps, function field, blow-up
  9. Tangent cone, tangent space, regular and singular points, smooth varieties, Jacobi criteria