Concept

Affine variety

Related lectures (31)

Affine Varieties

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Algebraic Curves: Normalization

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

Affine Algebraic Varieties: Zariski Topology

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.

Modern Algebraic Geometry

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

Affine varieties: additional observations

Covers coordinate rings, closed embeddings, and operations on affine varieties.

Affine Algebraic Sets

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

The Coordinate Ring of a Linearly Reductive Group

Covers the properties of the coordinate ring of a linearly reductive group.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Field of Rational Functions

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

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Smooth Projective Varieties

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

G-modules and G-varieties

Explores the embedding of chi-varieties into vector spaces with linear actions.

Isotypic Decomposition: Finitely Generated C-Algebras

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Topology of Riemann Surfaces

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

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Regular Functions on Quasi-Affine Varieties

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

Morphisms and Local Rings

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

The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Affine Varieties and Hypersurfaces

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

Projective Algebraic Sets: Definitions and Properties

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