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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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期刊全称An Undergraduate Primer in Algebraic Geometry
影响因子2023Ciro Ciliberto
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发行地址Provides 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
学科分类UNITEXT
图书封面Titlebook: An Undergraduate Primer in Algebraic Geometry;  Ciro Ciliberto Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusi
影响因子.This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems..The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology..This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic.. .The book contains several exercises, in which there are more examples and parts of the theory that are not fully
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Dimension,rt with the following: Let ., . be quasi-projective varieties with .. Then .. If, in addition, . is closed in . and ., then .. It suffices to reduce to the case in which . and . are affine. Then we may assume ., so that .(.) and .(.) are generated, as .-algebras, by .. Let .. Then any .-tuple . of e
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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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Projective Plane Curves,ct. . that if we have the decomposition in distinct irreducible components .then the curves ., ., are called the . of . and one writes ., where . is called the . of . in ., for .. Recall form Exercises . and . that if . is a point of . we defined the . . of . for .. We defined also the tangent cone
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An Undergraduate Primer in Algebraic Geometry978-3-030-71021-7Series ISSN 2038-5714 Series E-ISSN 2532-3318
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