arXiv Analytics

Sign in

arXiv:1010.0665 [math.AG]AbstractReferencesReviewsResources

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

Published 2010-10-04, updated 2012-01-24Version 3

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.

Comments: 19 pages
Categories: math.AG
Subjects: 14M25, 14P99
Related articles: Most relevant | Search more
arXiv:math/0206121 [math.AG] (Published 2002-06-12)
Hilbert functions of points on Schubert varieties in the Grassmannian
arXiv:math/0012079 [math.AG] (Published 2000-12-11)
Rational curves on Grassmannians: systems theory, reality, and transversality
arXiv:math/0501130 [math.AG] (Published 2005-01-10, updated 2007-01-29)
On the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0

Links

Toolbox