On degeneracy loci of equivariant bi-vector fields on a smooth toric variety
We study equivariant bi-vector fields on a toric variety. We prove that, on a smooth toric variety of dimension n, the locus where the rank of an equivariant bi-vector field is ≤ 2k is not empty and has at least a component of dimension ≥ 2k + 1, for all integers k > 0 such that 2k < n. The sa...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2019-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | http://www1.mat.uniroma1.it/ricerca/rendiconti/40_2_(2019)_81-95.html |
| _version_ | 1818300192493928448 |
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| author | Elena Martinengo |
| author_facet | Elena Martinengo |
| author_sort | Elena Martinengo |
| collection | DOAJ |
| description | We study equivariant bi-vector fields on a toric variety. We prove that, on a smooth toric variety of dimension n, the locus where the rank of an equivariant bi-vector field is ≤ 2k is not empty and has at least a component of dimension ≥ 2k + 1, for all integers k > 0 such that 2k < n. The same is true also for k = 0, if the toric variety is smooth and compact. While for the non compact case, the locus in question has to be assumed to be non empty. |
| first_indexed | 2024-12-13T05:03:13Z |
| format | Article |
| id | doaj.art-ea3fd2313ad44fddbead8954b1905bf8 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-12-13T05:03:13Z |
| publishDate | 2019-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-ea3fd2313ad44fddbead8954b1905bf82022-12-21T23:58:44ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502019-01-01408195On degeneracy loci of equivariant bi-vector fields on a smooth toric varietyElena Martinengo0Department of Mathematics "Giuseppe Peano", University of TurinWe study equivariant bi-vector fields on a toric variety. We prove that, on a smooth toric variety of dimension n, the locus where the rank of an equivariant bi-vector field is ≤ 2k is not empty and has at least a component of dimension ≥ 2k + 1, for all integers k > 0 such that 2k < n. The same is true also for k = 0, if the toric variety is smooth and compact. While for the non compact case, the locus in question has to be assumed to be non empty.http://www1.mat.uniroma1.it/ricerca/rendiconti/40_2_(2019)_81-95.htmlToric varietiesequivariant bi-vector fieldsPoisson manifold |
| spellingShingle | Elena Martinengo On degeneracy loci of equivariant bi-vector fields on a smooth toric variety Rendiconti di Matematica e delle Sue Applicazioni Toric varieties equivariant bi-vector fields Poisson manifold |
| title | On degeneracy loci of equivariant bi-vector fields on a smooth toric variety |
| title_full | On degeneracy loci of equivariant bi-vector fields on a smooth toric variety |
| title_fullStr | On degeneracy loci of equivariant bi-vector fields on a smooth toric variety |
| title_full_unstemmed | On degeneracy loci of equivariant bi-vector fields on a smooth toric variety |
| title_short | On degeneracy loci of equivariant bi-vector fields on a smooth toric variety |
| title_sort | on degeneracy loci of equivariant bi vector fields on a smooth toric variety |
| topic | Toric varieties equivariant bi-vector fields Poisson manifold |
| url | http://www1.mat.uniroma1.it/ricerca/rendiconti/40_2_(2019)_81-95.html |
| work_keys_str_mv | AT elenamartinengo ondegeneracylociofequivariantbivectorfieldsonasmoothtoricvariety |