Tangent Spaces in Algebraic Geometry

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

Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Explores the relationship between tangent spaces and dimension in algebraic geometry.

Explores finding the equation of the tangent line to a function's graph at a point.

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Introduces Lie algebras, vector spaces with a special bracket operation.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.