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Concept

Algebraic geometry and analytic geometry

Related lectures (31)

Varieties with nef anti-canonical: Surjective Albanese

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

Conformal Blocks: Functions on Moduli Spaces

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

Algebraic Curves: Normalization

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

Gothic Surfaces: Curvature, Development, and Stereotomy Log in to Mediaspace to watch this video

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

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

Cartier Divisors and Invertible Sheaves Log in to Mediaspace to watch this video

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Quotient Criterion Log in to Mediaspace to watch this video

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant 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.

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.

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.

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.

Tangent Spaces Insights Log in to Mediaspace to watch this video

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

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

Covers the study of graded modules and quasicoherent sheaves 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.

Adjunctions and Applications Log in to Mediaspace to watch this video

Covers adjunctions, projective varieties, regularity, and valuative criteria 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.

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.

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.

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.