Fundamentals of Algebraic Geometry. Set up (Noetherian rings), algebraic sets, correspondences between ideals and algebraic sets, Hilbert's Basis Theorem and Hilbert's Nullstellensatz.

Divisors and Line Bundles. Recalling the notion of a divisor in the context of sheaves. Defining line bundles, the Picard group and associated line bundles.

Describing canonical bundles as associated bundles, defining Iitake and Kodaira dimension and putting the adjunction formula into perspective for classification of surfaces in P_3. Introducing K3 surfaces and Quartics and Kummer surfaces as prominent examples.

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