GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION

被引：22

作者：

Leykin, Anton ^{[1
]}

Sottile, Frank ^{[2
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

MATHEMATICS OF COMPUTATION | 2009年 / 78卷 / 267期

关键词：

Polynomial homotopy continuation; Schubert problem; Galois group; ENUMERATIVE GEOMETRY; SYSTEMS; TRANSVERSALITY; ALGORITHMS; CALCULUS; REAL;

D O I：

10.1090/S0025-5718-09-02239-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in C-8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S-6006.

引用

页码：1749 / 1765

页数：17

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