Work

Restricted monodromy containing transpositions

Year: 2026

Type: preprint

Abstract: We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group significantly constrains the monodromy group of the original branched cover. Using this result, we complete the sparse trace test algorithm, which numerically verifies whether a set of solutions to a sparse polynomial system is complete. Along the way, we develop a generalization of the notion of a trace test in the setting of branched covers.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.23238

Authors: Barnhart, Julianne, Brysiewicz, Taylor, Burr, Michael, Yahl, Thomas

Institutions: Whitworth University, Clemson University, University of Wisconsin–Madison

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Natural Sciences and Engineering Research Council of Canada

Award: G4998900716

OpenAlex ID: W7214038039

Cites: 1

Cited by:

Related to: 10