Some lower bounds in the B. and M. Shapiro conjecture for flag varieties
Algebraic Geometry
2010-06-07 v2 Combinatorics
Abstract
The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile's monotonicity conditions are not satisfied.
Keywords
Cite
@article{arxiv.1006.0664,
title = {Some lower bounds in the B. and M. Shapiro conjecture for flag varieties},
author = {Monique Azar and Andrei Gabrielov},
journal= {arXiv preprint arXiv:1006.0664},
year = {2010}
}
Comments
21 pages, 6 figures, see also http://www.math.purdue.edu/~agabriel