Hilbert’s basis theorem, Hilbert‘s Nullstellensatz, (quasi-)affine and (quasi-)projective varieties, dimension, Zariski topology, local rings, morphisms and rational maps, blow-ups smoothness, intersection multiplicities, Bézout‘s theorem, plane curves and resolution of singularities, divisors and the Riemann-Roch theorem for curves
- Atiyah McDonald, Introduction to commutative Algebra,
- R. Hartshorne, Algebraic Geometry, Springer.
- K. Hulek Elementary Algebraic Geometry,
- M. Reid, Undergraduate Algebraic Geometry