Algebraic Varieties: Projective Sets and Topology

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Related lectures (35)

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.

Adjunctions and Applications Log in to Mediaspace to watch this video

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

Affine Varieties Log in to Mediaspace to watch this video

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

Applications of Serre Duality Log in to Mediaspace to watch this video

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

Algebraic Subsets of A^1 Log in to Mediaspace to watch this video

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Projective Space and Algebraic Sets Log in to Mediaspace to watch this video

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

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.

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.

The Regular Representation Log in to Mediaspace to watch this video

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

Plane Curves: Singular Points and Multiplicities Log in to Mediaspace to watch this video

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Algebraic Quotients Log in to Mediaspace to watch this video

Covers the concept of algebraic quotients in the context of a-variety.

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.

Dedekind Rings and Fractional Ideals Log in to Mediaspace to watch this video

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Dedekind Rings: Factorisation and Ideal Class Group Log in to Mediaspace to watch this video

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Tangent Spaces in Algebraic Geometry Log in to Mediaspace to watch this video

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

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