Tangent Spaces and Varieties

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Related lectures (35)

Varieties with nef anti-canonical: Surjective Albanese

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

Algebraic Curves: Normalization

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

Albanese Morphism: Kodaira Dimension Zero

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

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

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 Insights Log in to Mediaspace to watch this video

Explores the relationships between tangent spaces, dimensions, and sub-varieties 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.

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.

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.

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.

Adjunctions and Applications Log in to Mediaspace to watch this video

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

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.

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.

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.

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.

Modern Algebraic Geometry Log in to Mediaspace to watch this video

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

Algebraic Geometry: Forms and Maps Log in to Mediaspace to watch this video

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

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.

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