Galois groups of Schubert problems via homotopy computation

DOI10.1090/S0025-5718-09-02239-XzbMath1210.14064arXiv0710.4607MaRDI QIDQ3055169

Anton Leykin, Frank J. Sottile

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.4607

zbMATH Keywords

Galois grouppolynomial homotopy continuationSchubert problem

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Classical problems, Schubert calculus (14N15)

Related Items (16)

Certified Numerical Homotopy Tracking ⋮ Galois/Monodromy Groups for Decomposing Minimal Problems in 3D Reconstruction ⋮ A primal-dual formulation for certifiable computations in Schubert calculus ⋮ Classification of Schubert Galois groups in \(Gr(4, 9)\) ⋮ Certified predictor-corrector tracking for Newton homotopies ⋮ Computing monodromy via continuation methods on random Riemann surfaces ⋮ Robust certified numerical homotopy tracking ⋮ Using monodromy to avoid high precision in homotopy continuation ⋮ Numerical computation of Galois groups ⋮ Foreword. What is numerical algebraic geometry? ⋮ A lifted square formulation for certifiable Schubert calculus ⋮ Real monodromy action ⋮ A topological proof of the Shapiro-Shapiro conjecture ⋮ Homotopy continuation for the spectra of persistent Laplacians ⋮ Galois groups of Schubert problems of lines are at least alternating ⋮ Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm

Uses Software

• GAP
• HOM4PS
• PHCpack
• polymake
• Bertini

Cites Work

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• Interfacing with the Numerical Homotopy Algorithms in PHCpack
• Some real and unreal enumerative geometry for flag manifolds.

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