Rational functions and real Schubert calculus

DOI10.1090/S0002-9939-05-08048-2zbMath1110.14052arXivmath/0407408MaRDI QIDQ3372067

Alexandre Eremenko, Andrei Gabrielov, Michael Shapiro, A. D. Vaĭnshteĭn

Publication date: 17 February 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407408

zbMATH Keywords

Schubert calculusrational functionShapiro conjecture

Mathematics Subject Classification ID

Real algebraic sets (14P05) Classical problems, Schubert calculus (14N15) Real rational functions (26C15)

Related Items (17)

Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum ⋮ Spherical rectangles ⋮ Circular pentagons and real solutions of Painlevé VI equations ⋮ Metrics with conic singularities and spherical polygons ⋮ Wronskians, total positivity, and real Schubert calculus ⋮ Large deviations of multichordal \(\mathrm{SLE}_{0+}\), real rational functions, and zeta-regularized determinants of Laplacians ⋮ Reality property of discrete Wronski map with imaginary step ⋮ Some lower bounds in the B. and M. Shapiro conjecture for flag varieties ⋮ Disconjugacy and the secant conjecture ⋮ On total reality of meromorphic functions ⋮ On metrics of curvature 1 with four conic singularities on tori and on the sphere ⋮ Fuchsian equations with three non-apparent singularities ⋮ The Secant Conjecture in the Real Schubert Calculus ⋮ The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz ⋮ The Monotone Secant Conjecture in the Real Schubert Calculus ⋮ Metrics with four conic singularities and spherical quadrilaterals ⋮ Frontiers of reality in Schubert calculus

Cites Work

• Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
• The Wronski map and Grassmannians of real codimension 2 subspaces.
• Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro
• The special Schubert calculus is real
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