Weighted expansions for canonical desingularization / Shreeram S. Abhyankar ; with foreword by U. Orbanz.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 910.Publisher: Berlin ; New York : Springer-Verlag, 1982Description: 1 online resource (vii, 236 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540389927; 354038992XSubject(s): Geometry, Algebraic | Mappings (Mathematics) | Singularities (Mathematics) | Singularités (Mathématiques) | Geometry, Algebraic | Mappings (Mathematics) | Singularities (Mathematics) | Geometrische Singularität | Algebraische Geometrie | Géométrie algébrique | Applications (Mathématiques) | Singularités (Mathématiques)Genre/Form: Electronic books. Additional physical formats: Print version:: Weighted expansions for canonical desingularization.DDC classification: 516.35 LOC classification: QA3 | .L28 no. 910 | QA564Other classification: 31.51 Online resources: Click here to access online
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Includes bibliographical references and index.
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Notation -- Semigroups -- Strings -- Semigroup strings with restrictions -- Ordered semigroup strings with restrictions -- Strings on rings -- Indeterminate strings -- Indeterminate strings with restrictions -- Restricted degree and order for indeterminate strings -- Indexing strings -- Nets -- Semigroup nets with restrictions -- Ordered semigroup nets with restrictions -- Nets on rings -- Indeterminate nets -- Indeterminate nets with restrictions -- Restricted degree and order for indeterminate nets -- Prechips -- Isobars for prechips and Premonic polynomials -- Substitutions -- Substitutions with restrictions -- Coordinate nets and Monic polynomials -- Graded ring of a ring at an ideal -- Graded ring of a ring -- Graded rings at strings and nets and the notions of separatedness and regularity for strings and nets -- Inner products and further notions of separatedness and regularity for strings -- Inner products and further notions of separatedness and regularity for nets -- Weighted isobars and weighted initial forms -- Initial forms for regular strings -- Initial forms for regular strings and nets -- Protochips and parachips -- N-support of an indexing string for 2?N?6 -- Prescales -- Derived prescales -- Supports of prescales -- Protoscales -- Inner products for protoscales -- Scales and isobars -- Properties of derived prescales -- Isobars for derived scales -- Isobars and initial forms for scales -- Initial forms for scales and regular nets -- Isobars for protochips -- Initial forms for protochips and monic polynomials.