Modern Algebraic Geometry

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Related lectures (50)

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Varieties with nef anti-canonical: Surjective Albanese

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

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Modern Algebraic Geometry: Schemes and Affine Schemes Log in to Mediaspace to watch this video

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

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.

Affine Varieties and Hypersurfaces Log in to Mediaspace to watch this video

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

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

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

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.

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.

Adjunctions and Applications Log in to Mediaspace to watch this video

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

Homogeneous Ideals and Regular Rings Log in to Mediaspace to watch this video

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

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 Morphisms: Theory and Applications Log in to Mediaspace to watch this video

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Redly Constructed Morphisms Log in to Mediaspace to watch this video

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Affine Varieties Log in to Mediaspace to watch this video

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

Algebraic Varieties and Morphisms Log in to Mediaspace to watch this video

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

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.

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

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

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

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

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