An Undergraduate Primer in Algebraic Geometry

An Undergraduate Primer in Algebraic Geometry
Title An Undergraduate Primer in Algebraic Geometry PDF eBook
Author Ciro Ciliberto
Publisher Springer Nature
Pages 327
Release 2021-05-05
Genre Mathematics
ISBN 3030710211

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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 developed in the text. Of some exercises, there are solutions at the end of each chapter.

A Primer of Algebraic Geometry

A Primer of Algebraic Geometry
Title A Primer of Algebraic Geometry PDF eBook
Author Huishi Li
Publisher CRC Press
Pages 393
Release 2017-12-19
Genre Mathematics
ISBN 1482270331

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"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."

Undergraduate Commutative Algebra

Undergraduate Commutative Algebra
Title Undergraduate Commutative Algebra PDF eBook
Author Miles Reid
Publisher Cambridge University Press
Pages 172
Release 1995-11-30
Genre Mathematics
ISBN 9780521458894

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Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.

Algebraic Topology

Algebraic Topology
Title Algebraic Topology PDF eBook
Author Satya Deo
Publisher Springer
Pages 332
Release 2003-12-01
Genre Mathematics
ISBN 9386279134

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A Primer of Algebraic Geometry

A Primer of Algebraic Geometry
Title A Primer of Algebraic Geometry PDF eBook
Author Huishi Li
Publisher CRC Press
Pages 398
Release 2017-12-19
Genre Mathematics
ISBN 1351990950

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"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."

Introduction to Algebraic Geometry

Introduction to Algebraic Geometry
Title Introduction to Algebraic Geometry PDF eBook
Author Igor Kriz
Publisher Springer Nature
Pages 481
Release 2021-03-13
Genre Mathematics
ISBN 303062644X

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The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.

A First Course In Algebraic Geometry And Algebraic Varieties

A First Course In Algebraic Geometry And Algebraic Varieties
Title A First Course In Algebraic Geometry And Algebraic Varieties PDF eBook
Author Flaminio Flamini
Publisher World Scientific
Pages 326
Release 2023-02-13
Genre Mathematics
ISBN 1800612672

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This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material.