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Related lectures (32)

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Modern Algebraic Geometry

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

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.

Affine Varieties and Hypersurfaces

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

Differential of a Morphism

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Morphisms and Local Rings

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

Projective Algebraic Sets: Definitions and Properties

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Projective Morphisms: Theory and Applications

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

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Smooth Projective Varieties

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