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Tangent Spaces Insights
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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 in Algebraic Geometry
Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.
Tangent Spaces and Varieties
Explores the relationship between tangent spaces and dimension 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.
Variety Defined as the Closure of VCA
Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.
Adjunctions and Applications
Covers adjunctions, projective varieties, regularity, and valuative criteria 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.
Regularity and Geometric Meaning
Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.
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.
Modern Algebraic Geometry
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
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.
Affine Varieties and Hypersurfaces
Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.
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 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.
Projective Morphisms: Theory and Applications
Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.
Dimension of Algebraic Variety
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Smooth Projective Varieties
Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.
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