Introduction to Plane Algebraic Curves
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 t...
Gardado en:
| Autor Principal: | |
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| Outros autores: | |
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Series: | Mathematics and Statistics (Springer; 11649-ZDB-2-SMA)
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Trad. de : "Ebene algebraische Kurven" Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to plane algebraic curves, Ernst Kunz, 2005, Boston, Birkhäuser, 1 volume (xii-293 pages), 0-8176-4381-8 |
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| 100 | 1 | |a Kunz, Ernst, |d 1933-2021. | |
| 245 | 1 | 0 | |a Introduction to Plane Algebraic Curves |c by Ernst Kunz ; translated from the original German by Richard G. Belshoff. |
| 260 | |a Boston, MA : |b Birkhäuser Boston. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Mathematics and Statistics (Springer; 11649-ZDB-2-SMA) | |
| 500 | |a Trad. de : "Ebene algebraische Kurven" | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Courbes planes | ||
| 650 | |a Courbes algébriques | ||
| 650 | |a Singularités (mathématiques) | ||
| 700 | 1 | |a Belshoff, Richard G., |d 19..- |4 trl | |
| 765 | 0 | |t Ebene algebraische Kurven | |
| 776 | 0 | |0 094654034 |t Introduction to plane algebraic curves |f Ernst Kunz |d 2005 |c Boston |n Birkhäuser |p 1 volume (xii-293 pages) |z 0-8176-4381-8 | |
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| 997 | |0 938872 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||