On connectedness in the parametric geometry of numbers
Number Theory
2024-10-02 v4 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2312.16961,
title = {On connectedness in the parametric geometry of numbers},
author = {Yuming Wei and Han Zhang},
journal= {arXiv preprint arXiv:2312.16961},
year = {2024}
}
Comments
Incorporate referee's suggestions