The Secant Conjecture in the Real Schubert Calculus

Luis D. Garca-Puente; Nickolas Hein; Christopher Hillar; Abraham Martn Del Campo; James Ruffo; Frank Sottile; Zach Teitler

doi:10.1080/10586458.2012.661323

The Secant Conjecture in the Real Schubert Calculus

Luis D. Garca-Puente, Nickolas Hein, Christopher Hillar, Abraham Martn Del Campo, James Ruffo, Frank Sottile, Zach Teitler

Mathematics Department

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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
Pages (from-to)	252-265
Number of pages	14
Journal	Experimental Mathematics
Volume	21
Issue number	3
DOIs	https://doi.org/10.1080/10586458.2012.661323
State	Published - 11 Sep 2012

Keywords

14M25
14P99
Grassmannian
Schubert calculus
Shapiro conjecture

EGS Disciplines

Algebraic Geometry
Mathematics

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10.1080/10586458.2012.661323

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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.",

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T1 - The Secant Conjecture in the Real Schubert Calculus

AU - Garca-Puente, Luis D.

AU - Hein, Nickolas

AU - Hillar, Christopher

AU - Campo, Abraham Martn Del

AU - Ruffo, James

AU - Sottile, Frank

AU - Teitler, Zach

PY - 2012/9/11

Y1 - 2012/9/11

N2 - 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.

AB - 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.

KW - 14M25

KW - 14P99

KW - Grassmannian

KW - Schubert calculus

KW - Shapiro conjecture

UR - http://www.scopus.com/inward/record.url?scp=84866366601&partnerID=8YFLogxK

U2 - 10.1080/10586458.2012.661323

DO - 10.1080/10586458.2012.661323

M3 - Article

SN - 1058-6458

VL - 21

SP - 252

EP - 265

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 3

ER -

The Secant Conjecture in the Real Schubert Calculus

Abstract

Keywords

EGS Disciplines

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