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 language | American English |
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Journal | Mathematics Faculty Publications and Presentations |
State | Published - 11 Sep 2012 |
Keywords
- Grassmannian
- Schubert calculus
- Shapiro conjecture
EGS Disciplines
- Algebraic Geometry
- Mathematics