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.
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The second author was supported by the NSF grant DMS-0801050.
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Azar, M., Gabrielov, A. Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties. Discrete Comput Geom 46, 636–659 (2011). https://doi.org/10.1007/s00454-010-9314-8
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DOI: https://doi.org/10.1007/s00454-010-9314-8