The Secant Conjecture in the Real Schubert Calculus

Luis D. García-Puente, Nickolas Hein, Christopher Hillar, Abraham Martín del Campo, James Ruffo, Frank Sottile, Zach Teitler

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 11 Sep 2012

Keywords

  • Grassmannian
  • Schubert calculus
  • Shapiro conjecture

EGS Disciplines

  • Algebraic Geometry
  • Mathematics

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