Tangent Spaces and Varieties

Related lectures (32)

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

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

Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

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

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.