Lecture

Projective Space and Algebraic Sets

Related lectures (31)

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

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

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Projective Algebraic Sets: Definitions and Properties

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

Homogeneous Ideals and Regular Rings

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Affine Algebraic Sets

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

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Projective Varieties: An Algebraic Study

Covers the study of projective varieties and their relation to compact manifolds.

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.