Affine Varieties and Hypersurfaces

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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.

Plane Curves: Singular Points and Multiplicities

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Affine Varieties

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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.

Ideals and PPCM

Covers the concept of ideals in polynomial rings and their properties.

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.