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arXiv · 2312.16961

On connectedness in the parametric geometry of numbers

Yuming Wei·Han Zhang
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Abstract

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.

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Yuming Wei, Han Zhang. 2023-12-28. On connectedness in the parametric geometry of numbers. https://doi.org/10.2140/cnt.2024.13.299

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