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Lecture

Affine Algebraic Sets

In course

MATH-328: Algebraic geometry I - Curves

Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...

Description

This lecture introduces affine algebraic sets, starting with the definition of affine space and algebraic sets over a field. It covers the concept of hypersurfaces, affine planes, and elliptic curves, illustrating examples and properties of algebraic subsets. The lecture also discusses the relationship between ideals and algebraic sets, emphasizing the importance of the ground field being algebraically closed. Additionally, it explores the notion of Noetherian rings and modules, showcasing the finitely generated ideals and their corollary in algebraic varieties.

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Instructor

Dimitri Stelio Wyss

Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Geometry: Algebraic geometry

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