Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Introduces affine varieties and covers morphisms between them and their coordinate rings.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.
Covers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.
Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
