Projective Space and Algebraic Sets

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Related lectures (31)

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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.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Geometric Primary Decomposition

Covers radical ideals, Nullstellensatz, primary ideals, and 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.

Projective Spaces: Separation and Definitions

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Complements of Hypersurfaces in Projective Spaces

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Sum of RP2 Connected Sums

Covers the concept of connected sums in RP2 and how to compute them.

Algebraic Curves: Normalization

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

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.