Morphisms and Local Rings

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Related lectures (33)

Varieties with nef anti-canonical: Surjective Albanese

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

Albanese Morphism: Kodaira Dimension Zero

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

Modern Algebraic Geometry Log in to Mediaspace to watch this video

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

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.

Variety Defined as the Closure of VCA Log in to Mediaspace to watch this video

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

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.

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.

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 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.

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.

Regularity and Geometric Meaning Log in to Mediaspace to watch this video

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

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.

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.

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.

Primary Decomposition: Behaviour and Localisation Log in to Mediaspace to watch this video

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

Geometric Objects in Algebra Log in to Mediaspace to watch this video

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Lie Algebras: Introduction and Structure Log in to Mediaspace to watch this video

Introduces Lie algebras, vector spaces with a special bracket operation.

Weil Conjectures: Rationality and Function Equation Log in to Mediaspace to watch this video

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties 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.

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