Algebraic Geometry I

Topics

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

Literature

• Atiyah McDonald, Introduction to commutative Algebra,
  
• R. Hartshorne, Algebraic Geometry, Springer.
• K. Hulek Elementary Algebraic Geometry,
• M. Reid, Undergraduate Algebraic Geometry

Links to the books are found here.