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Israel Journal of Mathematics

, 136:353 | Cite as

Generalizations of the odd degree theorem and applications

  • Shmuel Friedland
  • Anatoly S. Libgober
Article

Abstract

LetV ⊂ ℙℝ n be an algebraic variety, such that its complexificationV ⊂ ℙ n is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ n of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.

Keywords

Tangent Bundle Algebraic Variety Euler Characteristic Chern Class Hyperplane Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    J. F. Adams,Vector fields on spheres, Annals of Mathematics75 (1962), 603–632.CrossRefMathSciNetGoogle Scholar
  2. [2]
    J. F. Adams, P. D. Lax and R. S. Phillips,On matrices whose real linear combinations are nonsingular, Proceedings of the American Mathematical Society16 (1965), 318–322.CrossRefMathSciNetGoogle Scholar
  3. [3]
    E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris,Geometry of Algebraic Curves,I, Grundlehren der mathematischen Wissenschaften, Vol. 267, Springer, New York, 1985.MATHGoogle Scholar
  4. [4]
    R. Bott and L. W. Tu,Differential Forms in Algebraic Topology, Graduate Texts, Vol. 82, Springer, New York, 1982.Google Scholar
  5. [5]
    D. Falikman, S. Friedland and R. Loewy,On spaces of matrices containing a nonzero matrix of bounded rank, Pacific Journal of Mathematics207 (2002), 157–176.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    S. Friedland and R. Loewy,Spaces of symmetric matrices containing a nonzero matrix of bounded rank, Linear Algebra and its Applications287 (1999), 161–170.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    W. Fulton,Intersection Theory, Springer, Berlin, 1984.MATHGoogle Scholar
  8. [8]
    P. Griffiths and J. Harris,Principles of Algebraic Geometry, Wiley, New York, 1978.MATHGoogle Scholar
  9. [9]
    J. Harris and L. W. Tu,On symmetric and skew-symmetric determinantal varieties, Topology23 (1984), 71–84.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    F. Hirzebruch,Topological Methods in Algebraic Geometry, Grundlehren der mathematischen Wissenschaften, Vol. 131, Springer, New York, 1966.Google Scholar

Copyright information

© Hebrew University 2003

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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