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Bibliographic Details
Main Authors: Wei, Yuming, Zhang, Han
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2312.16961
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Table of 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.