This webpage contains lecture notes, homeworks for algebraic geometry.
Lecture notes:
Lecture 1 (02.10.2020) Systems of equations, rings, ideals, quotient ring. Functor of points, category theory, Yoneda lemma.
Lecture 2 (09.10.2020) Noetherian condition, prime ideals, maximal ideals, radical, Spec, Zariski topology.
Lecture 3 (16.10.2020) Points, maximal ideals, closed points, geometric points, Specm, Nullstellensatz, ringed spaces, schemes.
Lecture 4 (23.10.2020) Irreducibility, minimal primes, height, dimension, more on construction of Spec as a ringed space.
Lecture 5 (30.10.2020) Proof of the sheaf property for the structure sheaf on Spec®. Heights of prime ideals and numbers of generators, localization.
Lecture 6 (06.11.2020) Local rings, Nakayama lemma, artinian rings, length. Proof of the Krull Hauptidealsatz. Dimension of the polynomial ring.
Lecture 7 (13.11.2020) Exercises. Schemes.
Lecture 8 (20.11.2020) Morphisms of schemes, affinization, gluing.
Lecture 9 (27.11.2020) More gluing. Proj.
Lecture 10 (04.12.2020) Prime ideals and points with coefficients in fields. Locally ringed spaces. More Proj.
Lecture 11 (11.12.2020) Proof that Proj is a scheme. Examples.
Lecture 12 (08.01.2021) More examples. Weighted projective spaces. Blowup. Curves on P2.
Lecture 13 (15.01.2021) Parametrization of conics. Functor of points. Fiber products.