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Author Garrity, Thomas A., 1959-

Title Algebraic geometry : a problem solving approach / Thomas Garrity, Richard Belshoff, Lynette Boos, Ryan Brown, Carl Lienert, David Murphy, Junalyn Navarra-Madsen, Pedro Poitevin, Shawn Robinson, Brian Snyder, Caryn Werner.

Published Providence, Rhode Island : American Mathematical Society ; Princeton, New Jersey : Institute for Advanced Study, [2013]


Location Call No. Status
 UniM Bund  516.35 GARR {Bund89 20200519}    AVAILABLE
Physical description xxii, 335 pages : illustrations ; 22 cm.
Series Student mathematical library. IAS/Park City mathematical subseries ; volume 66.
Student mathematical library. IAS/Park City mathematical subseries ; v. 66.
Bibliography Includes bibliographical references (pages 329-331) and index.
Contents Algebraic Geometry -- Overview -- Problem Book -- History of the Book -- Other Texts -- An Aside on Notation -- Acknowledgments -- 1.1.Conics over the Reals -- 1.2.Changes of Coordinates -- 1.3.Conics over the Complex Numbers -- 1.4.The Complex Projective Plane P2 -- 1.5.Projective Changes of Coordinates -- 1.6.The Complex Projective Line P1 -- 1.7.Ellipses, Hyperbolas, and Parabolas as Spheres -- 1.8.Links to Number Theory -- 1.9.Degenerate Conics -- 1.10.Tangents and Singular Points -- 1.11.Conics via Linear Algebra -- 1.12.Duality -- 2.1.Cubics in C2 -- 2.2.Inflection Points -- 2.3.Group Law -- 2.4.Normal Forms of Cubics -- 2.5.The Group Law for a Smooth Cubic in Canonical Form -- 2.6.Cross-Ratios and the j-Invariant -- 2.7.Torus as C/Λ -- 2.8.Mapping C/Λ to a Cubic -- 2.9.Cubics as Tori -- 3.1.Higher Degree Polynomials and Curves -- 3.2.Higher Degree Curves as Surfaces -- 3.3.Bézout's Theorem --
Contents note continued: 3.4.The Ring of Regular Functions and Function Fields -- 3.5.Divisors -- 3.6.The Riemann-Roch Theorem -- 3.7.Blowing Up -- 4.1.Zero Sets of Polynomials -- 4.2.Algebraic Sets and Ideals -- 4.3.Hilbert Basis Theorem -- 4.4.The Strong Nullstellensatz -- 4.5.The Weak Nullstellensatz -- 4.6.Points in Affine Space as Maximal Ideals -- 4.7.Affine Varieties and Prime Ideals -- 4.8.Regular Functions and the Coordinate Ring -- 4.9.Subvarieties -- 4.10.Function Fields -- 4.11.The Zariski Topology -- 4.12.Spec(R) -- 4.13.Points and Local Rings -- 4.14.Tangent Spaces -- 4.15.Dimension -- 4.16.Arithmetic Surfaces -- 4.17.Singular Points -- 4.18.Morphisms -- 4.19.Isomorphisms of Varieties -- 4.20.Rational Maps -- 4.21.Products of Affine Varieties -- 5.1.Definition of Projective Space -- 5.2.Graded Rings and Homogeneous Ideals -- 5.3.Projective Varieties -- 5.4.Functions, Tangent Spaces, and Dimension -- 5.5.Rational and Birational Maps -- 5.6.Proj(R) --
Contents note continued: 6.1.Intuition and Motivation for Sheaves -- 6.2.The Definition of a Sheaf -- 6.3.The Sheaf of Rational Functions -- 6.4.Divisors -- 6.5.Invertible Sheaves and Divisors -- 6.6.Basic Homology Theory -- 6.7.Cech Cohomology.
Subject Geometry, Algebraic.
ISBN 9780821893968 (paperback: alk. paper)