Modern Algebraic Geometry: Schemes and Affine Schemes

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Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.