Enumerative geometry for the real Grassmannian of lines in projective space

DOI10.1215/S0012-7094-97-08703-2zbMath0986.14033arXivalg-geom/9510017MaRDI QIDQ1355290

Frank J. Sottile

Publication date: 29 November 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9510017

zbMATH Keywords

Schubert varietiesGrassmannian of linesreal points of intersection

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items (19)

Certification for polynomial systems via square subsystems ⋮ The special Schubert calculus is real ⋮ On the cohomology rings of real flag manifolds: Schubert cycles ⋮ Halving spaces and lower bounds in real enumerative geometry ⋮ Real enumerative geometry and effective algebraic equivalence ⋮ Some remarks on real and complex output feedback ⋮ Enumeration of real conics and maximal configurations ⋮ Classification of Schubert Galois groups in \(Gr(4, 9)\) ⋮ Some lower bounds in the B. and M. Shapiro conjecture for flag varieties ⋮ Elementary transversality in the Schubert calculus in any characteristic ⋮ On total reality of meromorphic functions ⋮ Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro ⋮ Properties of four partial orders on standard Young tableaux ⋮ The Secant Conjecture in the Real Schubert Calculus ⋮ The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz ⋮ Random fields and the enumerative geometry of lines on real and complex hypersurfaces ⋮ Galois groups of Schubert problems of lines are at least alternating ⋮ Frontiers of reality in Schubert calculus ⋮ An arithmetic count of the lines meeting four lines in 𝐏³

Cites Work

• Dual equivalence with applications, including a conjecture of Proctor
• On Schensted's construction and the multiplication of Schur functions
• Filtrations on the homology of algebraic varieties
• Group characters and algebra
• The Hook Graphs of the Symmetric Group
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Enumerative geometry for the real Grassmannian of lines in projective space