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Exams/Learning aims
* Exam Oral examination
* Learning aims Our general scope is to present fundamental concepts related to the problem of solvings systems of polynomial equations. Algebraic Geometry studies these solutions from a “global” point of view, through the theory of Algebraic Varieties. We will define this important class of varieties and then we will study some of their most important properties and discuss key examples, which are fundamental for the whole theory. Learning aims are to give to students the following skills:
· working knowledge of basic elements of affine/projective geometry, of homomorphisms, isomorphisms and rational maps among algebraic varieties;
· familiarity with explicit examples, including plane curves, quadric surfaces, Grassmannian of lines, Veronese and Segre varieties, etc;
· if time permits, familiarity with the rich geometry of the canonical curve in terms of special linear series.