Projective Varieties: An Algebraic Study

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Explores the Albanese morphism of varieties with Kodaira dimension zero in positive characteristic.

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

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

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores the embedding of chi-varieties into vector spaces with linear actions.

Introduces the regular representation, a key tool for studying group actions on varieties.

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

Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.