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 flag manifolds and present massive 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.
Publié le : 2006-05-15
Classification:
Shapiro conjecture,
Schubert variety,
Grassmannian,
flag manifold,
14M15,
14N15,
14P99
@article{1175789741,
author = {Ruffo, Jim and Sivan, Yuval and Soprunova, Evgenia and Sottile, Frank},
title = {Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds},
journal = {Experiment. Math.},
volume = {15},
number = {1},
year = {2006},
pages = { 199-222},
language = {en},
url = {http://dml.mathdoc.fr/item/1175789741}
}
Ruffo, Jim; Sivan, Yuval; Soprunova, Evgenia; Sottile, Frank. Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds. Experiment. Math., Tome 15 (2006) no. 1, pp. 199-222. http://gdmltest.u-ga.fr/item/1175789741/