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Lecture
Tangent Spaces and Varieties
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Related lectures (32)
Tangent Spaces in Algebraic Geometry
Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.
Tangent Spaces Insights
Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.
Variety Defined as the Closure of VCA
Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.
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
Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.
Regularity and Geometric Meaning
Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.
Modern Algebraic Geometry: Schemes and Affine Schemes
Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.
Adjunctions and Applications
Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.
Weil Conjectures: Rationality and Function Equation
Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.
Primary Decomposition: Behaviour and Localisation
Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.
Riemann Zeta Function
Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.
Affine Varieties and Hypersurfaces
Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.
Projective Algebraic Sets: Definitions and Properties
Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.
Intersection Numbers: Algebraic Counting Solutions
Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.
Modern Algebraic Geometry
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Algebraic Geometry: Forms and Maps
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
Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.
Differential of a Morphism
Introduces the concept of the differential of a morphism and its applications in algebraic treatments.
Morphisms and Local Rings
Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.
Projective Varieties: Invariants and Dimensions
Covers invariants and dimensions of projective varieties, emphasizing their importance.
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