The Secant Conjecture in the real Schubert calculus

Details The Secant Conjecture in the real Schubert calculus The Secant Conjecture in the real Schubert calculus

2010-10-04

arxiv.org/abs/1010.0665v3

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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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