Projective Space and Algebraic Sets

Related lectures (31)

Page 3 of 4

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

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.

Explores homogeneous coordinates, conics like ellipses, hyperbolas, and parabolas, and rewriting equations.

Explores étale motivic cohomology and the Hodge conjecture with a focus on counter-examples.

Explores homogeneous coordinates, curves, and unique solutions in Cartesian coordinates.

Explores general conics, motor blocks, and homo coordinates in matrix decomposition and coefficient calculations.

Covers invariants and dimensions of projective varieties, emphasizing their importance.

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

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

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.