Concept

Complex projective space

Related lectures (19)

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

Elliptic Curves: Singular Points and Group Law

Explores singular points, the group law, and the ambiguity in defining the sum of a point with itself on elliptic curves.

Topology of Riemann Surfaces

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

Homology of Projective Space

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

Sum of RP2 Connected Sums

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

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Complements of Hypersurfaces in Projective Spaces

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

Incidence Geometry & Elliptic Curves

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Projective Space and Algebraic Sets

Introduces projective space and algebraic sets, discussing homogeneous coordinates, ideals, and generators.

Cell Attachment: Large Cell

Delves into cell attachment, exploring its implications for different cell dimensions.

Homogeneous Ideals and Regular Rings

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

Projective Spaces: Separation and Definitions

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

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Chain Homotopy and Projective Complexes

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Topology: Separation Criteria and Quotient Spaces

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

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Introduction to Euclidean Elements

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Modern Algebraic Geometry

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

Homology with coefficients

Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.