The Secant Conjecture in the Real Schubert Calculus Academic Article uri icon

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. © 2012 Copyright Taylor and Francis Group, LLC.

author list (cited authors)

  • García-Puente, L. D., Hein, N., Hillar, C., del Campo, A. M., Ruffo, J., Sottile, F., & Teitler, Z.

citation count

  • 9

publication date

  • September 2012