Concept
Affine variety
Related lectures (44)
Field of Rational Functions
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
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Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Regular Functions on Quasi-Affine Varieties
Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.
Algebraic Curves: Normalization
Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.
Affine Varieties and Hypersurfaces
Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.
Macdonald identities
Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.
Algebraic Varieties and Morphisms
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Affine Algebraic Varieties: Zariski Topology
Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.
Dimension of Algebraic Variety
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Morphisms between Affine Varieties
Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.