The Aluffi Algebra and Linearity Condition
The Aluffi algebra is an algebraic version of characteristic cycles in intersection theory which is an intermediate graded algebra between the symmetric algebra (naive blowup) and the Rees algebra (blowup). Let R be a commutative Noetherian ring and J ⊂I ideals of R. We say that J ⊂I satisfy line...
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| Format: | Article |
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Kharazmi University
2022-12-01
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| Series: | پژوهشهای ریاضی |
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| Online Access: | http://mmr.khu.ac.ir/article-1-3046-en.html |
| _version_ | 1827991160006639616 |
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| author | Abbas Nasrollah Nejad Parisa Solhi |
| author_facet | Abbas Nasrollah Nejad Parisa Solhi |
| author_sort | Abbas Nasrollah Nejad |
| collection | DOAJ |
| description | The Aluffi algebra is an algebraic version of characteristic cycles in intersection theory which is an intermediate graded algebra between the symmetric algebra (naive blowup) and the Rees algebra (blowup). Let R be a commutative Noetherian ring and J ⊂I ideals of R. We say that J ⊂I satisfy linearity condition if the Aluffi algebra of I/J is isomorphic with the symmetric algebra. In this paper, we present the necessary and sufficient conditions for satisfying linearity condition. We give classes of ideals J ⊂I which satisfy linearity condition. We prove that if J is a complete intersection ideal contained in I, then J ⊂I satisfy linearity condition if and only if the ideal I is of linear type. |
| first_indexed | 2024-04-10T00:46:12Z |
| format | Article |
| id | doaj.art-869635926173473eb46a874db42b2682 |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:46:12Z |
| publishDate | 2022-12-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-869635926173473eb46a874db42b26822023-03-13T19:26:42ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542022-12-0184137150The Aluffi Algebra and Linearity ConditionAbbas Nasrollah Nejad0Parisa Solhi1 Institute for Advanced Studies in Basic Sciences (IASBS) 444 Prof. Yousef Sobouti Blvd., Zanjan 45137-66731, Iran Mohaghegh َArdebili Universit The Aluffi algebra is an algebraic version of characteristic cycles in intersection theory which is an intermediate graded algebra between the symmetric algebra (naive blowup) and the Rees algebra (blowup). Let R be a commutative Noetherian ring and J ⊂I ideals of R. We say that J ⊂I satisfy linearity condition if the Aluffi algebra of I/J is isomorphic with the symmetric algebra. In this paper, we present the necessary and sufficient conditions for satisfying linearity condition. We give classes of ideals J ⊂I which satisfy linearity condition. We prove that if J is a complete intersection ideal contained in I, then J ⊂I satisfy linearity condition if and only if the ideal I is of linear type.http://mmr.khu.ac.ir/article-1-3046-en.htmlaluffi algebrablowup algebrasingularityideal of linear type |
| spellingShingle | Abbas Nasrollah Nejad Parisa Solhi The Aluffi Algebra and Linearity Condition پژوهشهای ریاضی aluffi algebra blowup algebra singularity ideal of linear type |
| title | The Aluffi Algebra and Linearity Condition |
| title_full | The Aluffi Algebra and Linearity Condition |
| title_fullStr | The Aluffi Algebra and Linearity Condition |
| title_full_unstemmed | The Aluffi Algebra and Linearity Condition |
| title_short | The Aluffi Algebra and Linearity Condition |
| title_sort | aluffi algebra and linearity condition |
| topic | aluffi algebra blowup algebra singularity ideal of linear type |
| url | http://mmr.khu.ac.ir/article-1-3046-en.html |
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