Galois group computation of Schubert problems

Anton Leykin and Frank Sottile

G(2,4) Description

This is a webpage dedicated to the project that applies methods of numerical algebraic geometry to the problems in enumerative algebraic geometry. 

The first part of the project resulted in the paper on Galois groups of Schubert problems via homotopy computation:
"... We use numerical homotopy continuation to investigate the problem 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 8-dimensional complex space meeting 15 fixed 5-planes non-trivially is the full symmetric group S6006."

Based on the initial results, we conjecture that the Galois group of every simple Schubert problem is the full symmetric group. As the continuation of the research in this direction we are planning to produce more evidence for this conjecture as well as to go beyond simple Schubert problems.

Anton Leykin and Frank Sottile, Galois groups of Schubert problems via homotopy computation, 18 pages. ArXiV:0710.4607.


Work of Sottile supported by the National Science Foundation under CAREER Grant DMS-0538734.
This work was also supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.
Last modified on 16 Dec 2007