Titlebook: An Undergraduate Primer in Algebraic Geometry; Ciro Ciliberto Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusi

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Smooth and Singular Points,Let . be an affine variety, with . and let . be a point of .. Let . be a line passing through ., so that . has parametric equations of the form .The polynomial system in .has the solution .. If the polynomials . are all identically 0, this means that . is contained in ..

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Divisors, Linear Equivalence, Linear Series,In this chapter . will be an irreducible projective plane curve and we will denote by . its smooth birational model. A point . of . will be sometimes called a . of . . at the point ..

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Morphisms,ery regular function ., the function . is regular on .. We will denote by .(., .) the set of all morphisms from . to .. It is clear that the identity is a morphism and the composition of two morphisms is a morphism.

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Product of Varieties,t of projective spaces is not a projective space. In this chapter we will give a structure of a projective variety on the product of projective spaces, which will make it possible to define the general concept of product of quasi–projective varieties.

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The Cayley Form,two projections . and .. Consider the subset . of . defined in the following way .. . is a closed subset of .. . is a closed subset of ., so it suffices to show that there is a closed subset . of . such that ..

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Ciro CilibertoProvides a self contained introduction to Algebraic Geometry for undergraduate students.Contains many exercises, some of them with solution.Useful for non-experts who want to learn the basics of Algeb

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