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" Introduction to algebraic geometry / "
Steven Dale Cutkosky.
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BL
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| Record Number
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850272
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| Main Entry
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Cutkosky, Steven Dale
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| Title & Author
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Introduction to algebraic geometry /\ Steven Dale Cutkosky.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2018]
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| Series Statement
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Graduate studies in mathematics ;; 188
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| Page. NO
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xii, 484 pages ;; 27 cm.
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| ISBN
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1470435187
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: 9781470435189
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Introduction -- A crash course in commutative algebra -- Affine varieties -- Projective varieties -- Regular and rational maps of quasi projective varieties -- Products -- The blow up of an ideal -- Finite maps of quasi projective varieties -- Dimension of quasi projective algebraic sets -- Zariski's main theorem -- Nonsingularity -- Sheaves -- Applications to regular and rational maps -- Divisors -- Dierential forms and the canonical divisor -- Schemes -- The degree of a projective variety -- Cohomology -- Curves -- An introduction to intersection theory -- Surfaces -- Ramication and etale maps -- Bertini's theorems and general fibers of maps.
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| Abstract
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This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic 0 and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
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| Subject
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Geometry, Algebraic.
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| Subject
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Algebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.).
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| Subject
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Algebraische Geometrie
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| Subject
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Geometrische Algebra
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| Subject
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Geometry, Algebraic.
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| Dewey Classification
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516.3/5
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| LC Classification
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QA564.C8794 2018
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| NLM classification
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14-01msc
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14-01.msc
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| Parallel Title
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Algebraic geometry
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