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Related lectures (32)

Varieties with nef anti-canonical: Surjective Albanese

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

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.

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.

Tangent Spaces and Varieties Log in to Mediaspace to watch this video

Explores the relationship between tangent spaces and dimension in algebraic geometry.

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.

Riemann Zeta Function Log in to Mediaspace to watch this video

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and 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.

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.

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.

Modern Algebraic Geometry Log in to Mediaspace to watch this video

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

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.

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.

Differential of a Morphism Log in to Mediaspace to watch this video

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

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

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

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.

Intersection Numbers: Algebraic Counting Solutions Log in to Mediaspace to watch this video

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

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.

Dimension of Algebraic Variety Log in to Mediaspace to watch this video

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Smooth Projective Varieties Log in to Mediaspace to watch this video

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

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