Abstract
We formulate the secant conjecture, which is a generalization of the Shapiro conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for this conjecture as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some of the phenomena we observed in our data.
Citation
Luis D. García-Puente. Nickolas Hein. Christopher Hillar. Abraham Martín del Campo. James Ruffo. Frank Sottile. Zach Teitler. "The Secant Conjecture in the Real Schubert Calculus." Experiment. Math. 21 (3) 252 - 265, 2012.
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