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arXiv:1006.0664 [math.AG]AbstractReferencesReviewsResources

Some lower bounds in the B. and M. Shapiro conjecture for flag varieties

Monique Azar, Andrei Gabrielov

Published 2010-06-03, updated 2010-06-04Version 2

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.

Comments: 21 pages, 6 figures, see also http://www.math.purdue.edu/~agabriel
Categories: math.AG, math.CO
Subjects: 14M15, 14N10, 14P99, 26C15, 30C15
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