Credits: 3 (3-0-0)
Description
Rings of polynomials and their quotients, local rings, DVR, modules, free modules, exact sequences. Affine algebraic sets, The Hilbert basis theorem. Hilbert’s Nullstellansatz. Affine varieties: Coordinate rings, polynomial maps, coordinate changes, rational functions. Local Properties of plane curves: Multiple points, tangent lines, multiplicities and local rings, intersection number. Projective varieties: projective algebraic sets, projective plane curves, linear systems of curves, Bezout’s theorem, Max Noether’s fundamental theorem and its applications. Variety, Morphisms and Rational maps: The Zariski topology, varieties and their morphism, dimension of varieties, rational maps. Resolution of sigularies: Blowing up a point in affine and projective planes, quadratic transformations and nonsingular models of curves.
Prerequisite Tree
flowchart TD
MTL755-1024[MTL755]
MTL755-1024 --- Or1025[Any one of]:::empty
Or1025 -.-> MTL105-1026[MTL105]
Or1025 -.-> MTL501-1027[MTL501]
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