Algebraic Varieties: Projective Sets and Topology

Related lectures (31)

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Covers invariants and dimensions of projective varieties, emphasizing their importance.

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

Covers the study of projective varieties and their relation to compact manifolds.

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Covers primary decomposition in commutative rings and its application in prime ideals.

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.