Experimentation and conjectures in the real Schubert calculus for flag manifolds
Algebraic Geometry
2010-03-29 v2
Abstract
The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for the flag manifold and present massive (15.76 gigahertz-years) computational experimentation in support of this refined conjecture. We also prove the conjecture in some special cases using discriminants and establish relationships between different cases of the conjecture.
Keywords
Cite
@article{arxiv.math/0507377,
title = {Experimentation and conjectures in the real Schubert calculus for flag manifolds},
author = {James Ruffo and Yuval Sivan and Evgenia Soprunova and Frank Sottile},
journal= {arXiv preprint arXiv:math/0507377},
year = {2010}
}
Comments
34 pages. Revised and one example removed. Expanded version of math.AG/0502040. Related WWW page http://www.math.tamu.edu/~sottile/pages/Flags/index.html