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Title
An undergraduate primer in algebraic geometry / Ciro Ciliberto.
ISBN
9783030710217 (electronic bk.)
3030710211 (electronic bk.)
3030710203
9783030710200
Publication Details
Cham : Springer, 2021.
Language
English
Description
1 online resource (xi, 327 pages)
Item Number
10.1007/978-3-030-71021-7 doi
Call Number
QA564
Dewey Decimal Classification
516.3/5
Summary
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 urwitz 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 et 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Series
Unitext ; 129.
1 Affine and projective algebraic sets
2 Basic notions of elimination theory and applications
3 Zariski closed subsets and ideals in the polynomials ring
4 Some topological properties
5 Regular and rational functions
6 Morphisms
7 Rational maps
8 Product of varieties
9 More on elimination theory
10 Finite morphisms
11 Dimension
12 The Cayley form
13 Grassmannians
14 Smooth and singular points
15 Power series
16 Affine plane curves
17 Projective plane curves
18 Resolution of singularities of curves
19 Divisors, linear equivalence, linear series
20 The Riemann-Roch Theorem.
