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arXiv · 1010.0665

The Secant Conjecture in the real Schubert calculus

Luis Garcia-Puente·Nickolas Hein·Christopher J. Hillar·Abraham Martin del Campo·James Ruffo·Frank Sottile·Zach Teitler
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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 it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.

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Luis Garcia-Puente, Nickolas Hein, Christopher J. Hillar, Abraham Martin del Campo, James Ruffo, Frank Sottile, Zach Teitler. 2010-10-04. The Secant Conjecture in the real Schubert calculus. https://arxiv.org/abs/1010.0665

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