Parametric Expansions of an Algebraic Variety Near Its Singularities II
The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. <i>Axioms</i> <b>2023</b>, <i>5</i>, 469, where we calculated parametric expansions of the three-dimensional alg...
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MDPI AG
2024-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/106 |
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| author | Alexander D. Bruno Alijon A. Azimov |
| author_facet | Alexander D. Bruno Alijon A. Azimov |
| author_sort | Alexander D. Bruno |
| collection | DOAJ |
| description | The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. <i>Axioms</i> <b>2023</b>, <i>5</i>, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula>, which appeared in theoretical physics, near its 3 singular points and near its one line of singular points. For that we used algorithms of Nonlinear Analysis: extraction of truncated polynomials, using the Newton polyhedron, their power transformations and Formal Generalized Implicit Function Theorem. Here we calculate parametric expansions of the manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> near its one more singular point, near two curves of singular points and near infinity. Here we use 3 new things: (1) computation in algebraic extension of the field of rational numbers, (2) expansions near a curve of singular points and (3) calculation of branches near infinity. |
| first_indexed | 2024-03-07T22:42:48Z |
| format | Article |
| id | doaj.art-9bdbaa6e902948069fef448911162d19 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:48Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-9bdbaa6e902948069fef448911162d192024-02-23T15:07:25ZengMDPI AGAxioms2075-16802024-02-0113210610.3390/axioms13020106Parametric Expansions of an Algebraic Variety Near Its Singularities IIAlexander D. Bruno0Alijon A. Azimov1Keldysh Institute of Applied Mathematics of RAS, 125047 Moscow, RussiaDepartment of Algebra and Geometry, Samarkand State University Named after Sh. Rashidov, Samarkand 140104, UzbekistanThe paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. <i>Axioms</i> <b>2023</b>, <i>5</i>, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula>, which appeared in theoretical physics, near its 3 singular points and near its one line of singular points. For that we used algorithms of Nonlinear Analysis: extraction of truncated polynomials, using the Newton polyhedron, their power transformations and Formal Generalized Implicit Function Theorem. Here we calculate parametric expansions of the manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> near its one more singular point, near two curves of singular points and near infinity. Here we use 3 new things: (1) computation in algebraic extension of the field of rational numbers, (2) expansions near a curve of singular points and (3) calculation of branches near infinity.https://www.mdpi.com/2075-1680/13/2/106algebraic varietysingular pointlocal parametrizationpower geometry |
| spellingShingle | Alexander D. Bruno Alijon A. Azimov Parametric Expansions of an Algebraic Variety Near Its Singularities II Axioms algebraic variety singular point local parametrization power geometry |
| title | Parametric Expansions of an Algebraic Variety Near Its Singularities II |
| title_full | Parametric Expansions of an Algebraic Variety Near Its Singularities II |
| title_fullStr | Parametric Expansions of an Algebraic Variety Near Its Singularities II |
| title_full_unstemmed | Parametric Expansions of an Algebraic Variety Near Its Singularities II |
| title_short | Parametric Expansions of an Algebraic Variety Near Its Singularities II |
| title_sort | parametric expansions of an algebraic variety near its singularities ii |
| topic | algebraic variety singular point local parametrization power geometry |
| url | https://www.mdpi.com/2075-1680/13/2/106 |
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