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Introduction to algebraic geometry / Steven Dale Cutkosky

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Graduate Studies in Mathematics ; 188Publisher: Providence, Rhode Island : American Mathematical Society, [2018]Copyright date: © 2018Description: 1 Online-RessourceISBN:
  • 9781470446703
Other title:
  • Algebraic geometry
Subject(s): Additional physical formats: 9781470435189 | Erscheint auch als: Introduction to algebraic geometry. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2018. xii, 484 SeitenDDC classification:
  • 516.3/5
MSC: MSC: *14-01 | 14A05 | 14A10 | 14E05 | 14C20 | 14F10 | 14F25 | 14H05 | 14J25RVK: RVK: SK 240LOC classification:
  • QA564
Online resources: Summary: 12.2. Resolution of singularities12.3. Valuations in algebraic geometry; 12.4. Factorization of birational maps; 12.5. Monomialization of maps; Chapter 13. Divisors; 13.1. Divisors and the class group; 13.2. The sheaf associated to a divisor; 13.3. Divisors associated to forms; 13.4. Calculation of some class groups; 13.5. The class group of a curve; 13.6. Divisors, rational maps, and linear systems; 13.7. Criteria for closed embeddings; 13.8. Invertible sheaves; 13.9. Transition functions; Chapter 14. Differential Forms and the Canonical Divisor; 14.1. Derivations and Kähler differentialsSummary: 2.6. Rational maps of affine varietiesChapter 3. Projective Varieties; 3.1. Standard graded algebras; 3.2. Projective varieties; 3.3. Grassmann varieties; 3.4. Regular functions and regular maps of quasi-projective varieties; Chapter 4. Regular and Rational Maps of Quasi-projective Varieties; 4.1. Criteria for regular maps; 4.2. Linear isomorphisms of projective space; 4.3. The Veronese embedding; 4.4. Rational maps of quasi-projective varieties; 4.5. Projection from a linear subspace; Chapter 5. Products; 5.1. Tensor products; 5.2. Products of varieties; 5.3. The Segre embeddingSummary: 5.4. Graphs of regular and rational mapsChapter 6. The Blow-up of an Ideal; 6.1. The blow-up of an ideal in an affine variety; 6.2. The blow-up of an ideal in a projective variety; Chapter 7. Finite Maps of Quasi-projective Varieties; 7.1. Affine and finite maps; 7.2. Finite maps; 7.3. Construction of the normalization; Chapter 8. Dimension of Quasi-projective Algebraic Sets; 8.1. Properties of dimension; 8.2. The theorem on dimension of fibers; Chapter 9. Zariski's Main Theorem; Chapter 10. Nonsingularity; 10.1. Regular parameters; 10.2. Local equations; 10.3. The tangent spaceSummary: 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. MorePPN: PPN: 1032021624Package identifier: Produktsigel: ZDB-4-NLEBK
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