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The Resource Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)
Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)
Resource Information
The item Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Most important to this text: * Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves * Presents residue theory in the affine plane and its applications to intersection theory * Methods of proof for the Riemann–Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings * Examples, exercises, figures and suggestions for further study round out this fairly selfcontained textbook From a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students... The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time... One simply cannot do better in writing such a textbook." —Zentralblatt MATH
 Language

 eng
 eng
 Edition
 1st ed. 2005.
 Extent
 1 online resource (284 p.)
 Note
 Description based upon print version of record
 Contents

 Plane Algebraic Curves
 Ane Algebraic Curves
 Projective Algebraic Curves
 The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves
 Rational Functions on Algebraic Curves
 Intersection Multiplicity and Intersection Cycle of Two Curves
 Regular and Singular Points of Algebraic Curves. Tangents
 More on Intersection Theory. Applications
 Rational Maps. Parametric Representations of Curves
 Polars and Hessians of Algebraic Curves
 Elliptic Curves
 Residue Calculus
 Applications of Residue Theory to Curves
 The RiemannRoch Theorem
 The Genus of an Algebraic Curve and of Its Function Field
 The Canonical Divisor Class
 The Branches of a Curve Singularity
 Conductor and Value Semigroup of a Curve Singularity
 Isbn
 9780817644437
 Label
 Introduction to Plane Algebraic Curves
 Title
 Introduction to Plane Algebraic Curves
 Statement of responsibility
 by Ernst Kunz
 Language

 eng
 eng
 Summary
 This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Most important to this text: * Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves * Presents residue theory in the affine plane and its applications to intersection theory * Methods of proof for the Riemann–Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings * Examples, exercises, figures and suggestions for further study round out this fairly selfcontained textbook From a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students... The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time... One simply cannot do better in writing such a textbook." —Zentralblatt MATH
 http://library.link/vocab/creatorName
 Kunz, Ernst
 Dewey number

 516.3
 516.352
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 emJCB133wU
 Language note
 English
 LC call number
 QA564609
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/subjectName

 Geometry, algebraic
 Algebraic topology
 Mathematics
 Algebra
 Field theory (Physics)
 Algebraic Geometry
 Algebraic Topology
 Applications of Mathematics
 Commutative Rings and Algebras
 Associative Rings and Algebras
 Field Theory and Polynomials
 Label
 Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [285]287) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Plane Algebraic Curves  Ane Algebraic Curves  Projective Algebraic Curves  The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves  Rational Functions on Algebraic Curves  Intersection Multiplicity and Intersection Cycle of Two Curves  Regular and Singular Points of Algebraic Curves. Tangents  More on Intersection Theory. Applications  Rational Maps. Parametric Representations of Curves  Polars and Hessians of Algebraic Curves  Elliptic Curves  Residue Calculus  Applications of Residue Theory to Curves  The RiemannRoch Theorem  The Genus of an Algebraic Curve and of Its Function Field  The Canonical Divisor Class  The Branches of a Curve Singularity  Conductor and Value Semigroup of a Curve Singularity
 Dimensions
 unknown
 Edition
 1st ed. 2005.
 Extent
 1 online resource (284 p.)
 Form of item
 online
 Isbn
 9780817644437
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/0817644431
 Specific material designation
 remote
 System control number

 (CKB)1000000000492018
 (EBL)973759
 (OCoLC)828795113
 (SSID)ssj0000318498
 (PQKBManifestationID)11247233
 (PQKBTitleCode)TC0000318498
 (PQKBWorkID)10310818
 (PQKB)10132110
 (DEHe213)9780817644437
 (MiAaPQ)EBC973759
 (EXLCZ)991000000000492018
 Label
 Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [285]287) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Plane Algebraic Curves  Ane Algebraic Curves  Projective Algebraic Curves  The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves  Rational Functions on Algebraic Curves  Intersection Multiplicity and Intersection Cycle of Two Curves  Regular and Singular Points of Algebraic Curves. Tangents  More on Intersection Theory. Applications  Rational Maps. Parametric Representations of Curves  Polars and Hessians of Algebraic Curves  Elliptic Curves  Residue Calculus  Applications of Residue Theory to Curves  The RiemannRoch Theorem  The Genus of an Algebraic Curve and of Its Function Field  The Canonical Divisor Class  The Branches of a Curve Singularity  Conductor and Value Semigroup of a Curve Singularity
 Dimensions
 unknown
 Edition
 1st ed. 2005.
 Extent
 1 online resource (284 p.)
 Form of item
 online
 Isbn
 9780817644437
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/0817644431
 Specific material designation
 remote
 System control number

 (CKB)1000000000492018
 (EBL)973759
 (OCoLC)828795113
 (SSID)ssj0000318498
 (PQKBManifestationID)11247233
 (PQKBTitleCode)TC0000318498
 (PQKBWorkID)10310818
 (PQKB)10132110
 (DEHe213)9780817644437
 (MiAaPQ)EBC973759
 (EXLCZ)991000000000492018
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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