Concept

Glossary of algebraic geometry

Related lectures (31)

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.

Cartier Divisors and Invertible Sheaves

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

Tangent Spaces in Algebraic Geometry

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

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.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Redly Constructed Morphisms

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Motivic Knot Theory: Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, oriented links, intersection theory, and examples like the Hopf and Solomon links.

Quotient Criterion

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

Locally Noetherian Schemes

Covers the concept of locally Noetherian schemes in algebraic geometry.

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Tangent Spaces Insights

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

Adjunctions and Applications

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

Primary Decomposition: Behaviour and Localisation

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.

Projective Morphisms: Theory and Applications

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

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.

Differential of a Morphism

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

The Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Conformal Blocks: Functions on Moduli Spaces

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

Position Space Approach: Analyzing Banana Feynman Diagrams

Presents the position space approach to banana Feynman diagrams and their differential equations.