Primary Decomposition: Behaviour and Localisation

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Smooth Projective Varieties

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Cartier Divisors and Invertible Sheaves

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

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Tangent Spaces and Varieties

Explores the relationship between tangent spaces and dimension in algebraic geometry.

Tangent Spaces in Algebraic Geometry

Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.

Tangent Spaces in Algebraic Geometry

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

Geometric Objects in Algebra

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

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Algebraic Varieties and Morphisms

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.