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Algebraic Geometry written by Alexei Skorobogatov
. This is an other book of mathematics cover the following topics.

Basics of commutative algebra Integral closure. Noetherian rings, Noether’s normalization and Nullstellensatz

Affine geometry Zariski topology, Category of affine varieties, Examples of rational varieties, Smooth and singular points, Dimension. Application: Tsen’s theorem

Projective geometry Projective varieties, Morphisms of projective varieties

Local geometry Localization, local rings, DVR, Regular local rings, Geometric consequences of unique factorization in OP

Divisors The Picard group, Automorphisms of Pnk and of Ank, The degree of the divisor of a rational function on a projective curve, Bezout theorem for curves, Riemann–Roch theorem, From algebraic curves to error correcting codes

A More algebra Krull’s intersection theorem, Completion, The topological space Spec(R)

B More geometry Finite morphisms, Functoriality of Pic