On connectedness in the parametric geometry of numbers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914961580621824 |
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| author | Wei, Yuming Zhang, Han |
| author_facet | Wei, Yuming Zhang, Han |
| contents | Via multilinear algebra, we formulate a criterion for connectedness in the parametric geometry of numbers in terms of pencils, which are certain algebraic varieties in the space of matrices. As a consequence, we obtain a connectedness result for generic lattices arising from Diophantine approximation on analytic submanifolds, and sharpen Schmidt and Summerer's results of connectedness on simultaneous Diophantine approximation and approximation by linear forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On connectedness in the parametric geometry of numbers Wei, Yuming Zhang, Han Number Theory Dynamical Systems 11H06, 11J13, 37B05 Via multilinear algebra, we formulate a criterion for connectedness in the parametric geometry of numbers in terms of pencils, which are certain algebraic varieties in the space of matrices. As a consequence, we obtain a connectedness result for generic lattices arising from Diophantine approximation on analytic submanifolds, and sharpen Schmidt and Summerer's results of connectedness on simultaneous Diophantine approximation and approximation by linear forms. |
| title | On connectedness in the parametric geometry of numbers |
| topic | Number Theory Dynamical Systems 11H06, 11J13, 37B05 |
| url | https://arxiv.org/abs/2312.16961 |