Algebraic Varieties and Morphisms

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Related lectures (32)

Albanese Morphism: Kodaira Dimension Zero

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

Varieties with nef anti-canonical: Surjective Albanese

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

Discrete Log Problem: Index Calculus

Explores the discrete log problem and index calculus method in cryptography.

Modern Algebraic Geometry Log in to Mediaspace to watch this video

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Affine Varieties Log in to Mediaspace to watch this video

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Adjunctions and Applications Log in to Mediaspace to watch this video

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

Projective Varieties: Invariants and Dimensions Log in to Mediaspace to watch this video

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

Complex Manifolds: GAGA Principle Log in to Mediaspace to watch this video

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Projective Algebraic Sets: Definitions and Properties Log in to Mediaspace to watch this video

Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.

Morphisms and Local Rings Log in to Mediaspace to watch this video

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

Field of Rational Functions Log in to Mediaspace to watch this video

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

Regular Functions on Quasi-Affine Varieties Log in to Mediaspace to watch this video

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

Algebraic Varieties: Projective Sets and Topology Log in to Mediaspace to watch this video

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Projective Varieties: An Algebraic Study Log in to Mediaspace to watch this video

Covers the study of projective varieties and their relation to compact manifolds.

Morphisms between Affine Varieties Log in to Mediaspace to watch this video

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Smooth Projective Varieties Log in to Mediaspace to watch this video

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

Automorphisms of Projective Varieties Log in to Mediaspace to watch this video

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Affine Algebraic Sets Log in to Mediaspace to watch this video

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Algebraic Varieties in Linear Algebra Log in to Mediaspace to watch this video

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

The Regular Representation Log in to Mediaspace to watch this video

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

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