The Secant Conjecture in the real Schubert calculus Institutional Repository Document 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 it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.

author list (cited authors)

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

complete list of authors

  • Garcia-Puente, Luis||Hein, Nickolas||Hillar, Christopher J||del Campo, Abraham Martin||Ruffo, James||Sottile, Frank||Teitler, Zach

Book Title

  • arXiv

publication date

  • October 2010