The Resource Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres
Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres
Resource Information
The item Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
This item is available to borrow from 1 library branch.
- Summary
- This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi
- Language
- eng
- Extent
- 1 online resource (717 pages)
- Contents
-
- Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem
- 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations
- 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes
- Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem
- 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes
- Isbn
- 9780691096797
- Label
- Algebraic curves over a finite field
- Title
- Algebraic curves over a finite field
- Statement of responsibility
- J.W.P. Hirschfeld, G. Korchmaros, F. Torres
- Language
- eng
- Summary
- This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi
- Cataloging source
- E7B
- http://library.link/vocab/creatorDate
- 1940-
- http://library.link/vocab/creatorName
- Hirschfeld, J. W. P.
- Dewey number
- 516.352
- Index
- index present
- Language note
- In English
- LC call number
- QA565
- LC item number
- .H577 2008eb
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorName
-
- Korchmáros, G.
- Torres, F.
- Series statement
- Princeton Series in Applied Mathematics
- http://library.link/vocab/subjectName
-
- Curves, Algebraic
- Finite fields (Algebra)
- MATHEMATICS
- MATHEMATICS
- Curves, Algebraic
- Finite fields (Algebra)
- Galois-Feld
- Algebraische Kurve
- Label
- Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem
- 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations
- 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes
- Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem
- 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes
- Control code
- 889240929
- Dimensions
- unknown
- Extent
- 1 online resource (717 pages)
- Form of item
- online
- Isbn
- 9780691096797
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1515/9781400847419
- http://library.link/vocab/ext/overdrive/overdriveId
- 630111
- Specific material designation
- remote
- System control number
- (OCoLC)889240929
- Label
- Algebraic curves over a finite field, J.W.P. Hirschfeld, G. Korchmaros, F. Torres
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem
- 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations
- 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes
- Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem
- 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes
- Control code
- 889240929
- Dimensions
- unknown
- Extent
- 1 online resource (717 pages)
- Form of item
- online
- Isbn
- 9780691096797
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1515/9781400847419
- http://library.link/vocab/ext/overdrive/overdriveId
- 630111
- Specific material designation
- remote
- System control number
- (OCoLC)889240929
Subject
- Curves, Algebraic
- Finite fields (Algebra)
- Finite fields (Algebra)
- Galois-Feld
- MATHEMATICS -- Algebra | Abstract
- MATHEMATICS -- Geometry | General
- Curves, Algebraic
- Algebraische Kurve
Member of
- Princeton series in applied mathematics
- Ebook Central Academic Complete
- EBSCO eBook Public Library Collection-North America
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