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2000 Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro
Frank Sottile
Experiment. Math. 9(2): 161-182 (2000).

Abstract

Boris and Michael Shapiro have a conjecture concerning the Schubert calculus and real enumerative geometry and which would give infinitely many families of zero-dimensional systems of real polynomials (including families of overdetermined systems--all of whose solutions are real. It has connections to the pole placement problem in linear systems theory and to totally positive matrices. We give compelling computational evidence for its validity, prove it for infinitely many families of enumerative problems, show how a simple version implies more general versions, and present a counterexample to a general version of their conjecture.

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Frank Sottile. "Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro." Experiment. Math. 9 (2) 161 - 182, 2000.

Information

Published: 2000
First available in Project Euclid: 22 February 2003

zbMATH: 0997.14016
MathSciNet: MR1780204

Subjects:
Primary: 14N15
Secondary: 14M15 , 14P99

Keywords: enumerative geometry , Grassmannian , Gröbner basis , overdetermined system , total positivity

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 2 • 2000
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