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Generalizations of the odd degree theorem and applications

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Abstract

LetV ⊂ ℙℝn be an algebraic variety, such that its complexificationV ℂ ⊂ ℙn is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝn 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.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St., 60607, Chicago, IL, USA

    Shmuel Friedland & Anatoly S. Libgober

Authors
  1. Shmuel Friedland
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  2. Anatoly S. Libgober
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Correspondence to Shmuel Friedland.

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Friedland, S., Libgober, A.S. Generalizations of the odd degree theorem and applications. Isr. J. Math. 136, 353–371 (2003). https://doi.org/10.1007/BF02807205

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  • DOI: https://doi.org/10.1007/BF02807205

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