Tangent Spaces in Algebraic Geometry

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Page 2 of 4

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

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

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

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

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Explores differentiability in functions and tangent planes to surfaces.

Explores directional derivatives in two-variable functions and extremum points.