Toward a salmon conjecture
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2010
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908594581012480 |
|---|---|
| author | Bates, Daniel J. Oeding, Luke |
| author_facet | Bates, Daniel J. Oeding, Luke |
| contents | By using a result from the numerical algebraic geometry package Bertini we show that (up to high numerical accuracy) a specific set of degree 6 and degree 9 polynomials cut out the secant variety $σ_{4}(\mathbb{P}^{2}\times \mathbb{P} ^{2} \times \mathbb{P} ^{3})$. This, combined with an argument provided by Landsberg and Manivel (whose proof was corrected by Friedland), implies set-theoretic defining equations in degrees 5, 6 and 9 for a much larger set of secant varieties, including $σ_{4}(\mathbb{P}^{3}\times \mathbb{P} ^{3} \times \mathbb{P} ^{3})$ which is of particular interest in light of the salmon prize offered by E. Allman for the ideal-theoretic defining equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1009_6181 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Toward a salmon conjecture Bates, Daniel J. Oeding, Luke Algebraic Geometry 14L30, 13A50, 14M12, 20G05, 15A72, 15A69 By using a result from the numerical algebraic geometry package Bertini we show that (up to high numerical accuracy) a specific set of degree 6 and degree 9 polynomials cut out the secant variety $σ_{4}(\mathbb{P}^{2}\times \mathbb{P} ^{2} \times \mathbb{P} ^{3})$. This, combined with an argument provided by Landsberg and Manivel (whose proof was corrected by Friedland), implies set-theoretic defining equations in degrees 5, 6 and 9 for a much larger set of secant varieties, including $σ_{4}(\mathbb{P}^{3}\times \mathbb{P} ^{3} \times \mathbb{P} ^{3})$ which is of particular interest in light of the salmon prize offered by E. Allman for the ideal-theoretic defining equations. |
| title | Toward a salmon conjecture |
| topic | Algebraic Geometry 14L30, 13A50, 14M12, 20G05, 15A72, 15A69 |
| url | https://arxiv.org/abs/1009.6181 |