The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. This is the first semester of a two-semester sequence on Algebraic Geometry. Familiarity with the following topics is helpful though not strictly necessary: Basic notions of category theory: Yoneda Lemma, (co)limits, (co)products calculus on manifolds, including vector fields, differential forms and de Rham cohomology beginning graduate topology: (co)homology, fundamental groups, topological vector bundles complex analysis: Compact Riemann surfaces. In addition, students should understand the basic notions of commutative algebra, such as localization, Noetherian property and prime ideals. There are no prerequisite courses, but 18.705 Commutative Algebra must be taken concurrently. Smith, K.E, Kahanpää, L, Kekäläinen, P & Traves, W.Lectures: 2 sessions / week, 1.5 hours / session Prerequisites Shafarevich, I.R., Basic Algebraic Geometry 1, second edition, Springer-Verlag (1994).Student Texts 12, Cambridge University Press (2010)
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