The Resource Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)

Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)

Label
Introduction to Plane Algebraic Curves
Title
Introduction to Plane Algebraic Curves
Statement of responsibility
by Ernst Kunz
Creator
Author
Author
Subject
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 self-contained 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
Member of
http://library.link/vocab/creatorName
Kunz, Ernst
Dewey number
  • 516.3
  • 516.352
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
emJC-B133wU
Language note
English
LC call number
QA564-609
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)
Instantiates
Publication
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 Riemann-Roch 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
10.1007/0-8176-4443-1
Specific material designation
remote
System control number
  • (CKB)1000000000492018
  • (EBL)973759
  • (OCoLC)828795113
  • (SSID)ssj0000318498
  • (PQKBManifestationID)11247233
  • (PQKBTitleCode)TC0000318498
  • (PQKBWorkID)10310818
  • (PQKB)10132110
  • (DE-He213)978-0-8176-4443-7
  • (MiAaPQ)EBC973759
  • (EXLCZ)991000000000492018
Label
Introduction to Plane Algebraic Curves, by Ernst Kunz, (electronic resource)
Publication
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 Riemann-Roch 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
10.1007/0-8176-4443-1
Specific material designation
remote
System control number
  • (CKB)1000000000492018
  • (EBL)973759
  • (OCoLC)828795113
  • (SSID)ssj0000318498
  • (PQKBManifestationID)11247233
  • (PQKBTitleCode)TC0000318498
  • (PQKBWorkID)10310818
  • (PQKB)10132110
  • (DE-He213)978-0-8176-4443-7
  • (MiAaPQ)EBC973759
  • (EXLCZ)991000000000492018

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